Angle facts

Calculate the value of x.

You must show all your working.

In the diagram below:

• EG is a straight line • FGH is an isosceles triangle.

Calculate the value of x.

Find the size of angle a.

Find the size of angle b. Circle your answer.

55° 115° 120° 125° 135°

The diagram below shows some tiles in part of a tessellation. The tiles are all identical regular hexagons. Each of the interior angles is 120°.

Explain why the tiles tessellate.

You must give a reason, based on angle facts, for your answer.

Explain why tiles that are identical regular pentagons will not tessellate.

You must show working to support your explanation.

In the diagram below:

• EG is a straight line • FGH is an isosceles triangle.

Calculate the value of x.

Find the size of angle a.

Find the size of angle b. Circle your answer.

55° 115° 120° 125° 135°

Explain why tiles that are identical regular pentagons will not tessellate.

You must show working to support your explanation.

The points A, B and C lie on the circumference of a circle.

The straight line DCE is a tangent to the circle. AB = BC. ACB = x, where x is measured in degrees.

Find an expression for the size of ACD. Give your answer in terms of x.

You must give a reason for each step of your solution.

Calculate the size of angle x.

PQRS is a quadrilateral. QRT is a straight line.

Calculate the size of angle y.

The interior angle of a regular polygon is 171°.

How many sides does the polygon have?

A, B, C and D are points on the circumference of a circle with centre O.

Calculate the value of x.

Circle your answer.

55° 70° 110° 125° 135°

The interior angle of a regular polygon is 171°.

How many sides does the polygon have?

In the diagram below, A B C is a right-angled triangle and C D E is an isosceles triangle.

A B C = 90°, B A C = 64° and C D = C E. A D and B E are straight lines intersecting at C.

Calculate the size of each of the angles x, y and z.

Points A, B, C, D lie on a circle.

The line F A E is a tangent to the circle at A. B C D = 114°. D B A = x°. B A E = 2x°.

Calculate the value of x.

You must state any circle theorems that you use.

The points B, C, D and E lie on the circumference of a circle, with centre O. AF is a tangent to the circle. AO is a straight line.

Explain how you know that AOB is a right-angled triangle.

Calculate the size of angle x.

You must show all your working.

In the following diagram:

• CB and DE are parallel • CE and BD are straight lines • CA = AE.

Prove that triangles ABC and ADE are congruent.

You must show all your working and explain your reasoning.

Calculate the length of CE.

You must show all your working.

Hence, calculate the area of triangle CGE.

Find the size of each of the angles a, b and c.

Find the size of each of the angles a, b and c.

What percentage of the whole circle is shaded?

You must show how you calculated your answer.

What tangent property of circles did you use in order to answer part (a)?

Calculate the value of x.

The diagram below shows an isosceles triangle.

Calculate the value of y.

A regular polygon has 15 sides.

Calculate the size of an exterior angle of this regular polygon.

Calculate the value of x.

Hence find the length DE.

What percentage of the whole circle is shaded?

You must show how you calculated your answer.

What tangent property of circles did you use in order to answer part (a)?

In the diagram below, AD is a straight line.

BAC = 90°, BDE = 90° and CBE = 90°.

AC = 7·7 cm, BC = 11·3 cm and BD = 13·1 cm.

Calculate the value of x.

Hence find the length DE.

ABCDE is a regular pentagon with sides of length 11 cm. CDE is a sector of a circle with centre D and radius 11 cm. The two shapes are joined together, as shown below.

In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Calculate the length of the arc CE shown in the diagram.

You must show all your working.

In a shape similar to the one shown on the previous page, the regular pentagon has sides of length 671 cm.

Complete the following statement.

Total area of new shape = ………………………… × total area of original shape

You must show all your working.

In triangle ABC shown below, AB = 13 cm and BC = 11 cm.

D is a point on AC where BD = 7 cm and DC = 5 cm.

Calculate the size of BAD.

You must show all your working.

Calculate the value of y.

P, Q and R are points on the circumference of a circle with centre O.

Calculate the value of x. You must state all the angle properties that you use.

You must show all your working.

P, Q and R are points on the circumference of a circle with centre O.

Calculate the value of x. You must state all the angle properties that you use.

You must show all your working.

In the following diagram, the lines AC and BD bisect each other.

Prove that triangles ABE and CDE are congruent.

You must state the condition of congruence.

Calculate the size of angle x.

You must show all your working.

What is the special name given to the perimeter of a circle?

Circle the correct answer.

diameter radius chord tangent circumference

One of the following angles is a reflex angle.

Circle the correct answer.

70° 170° 270° 370° 470°

The diagram below shows two angles on a straight line. The larger angle is 30° greater than the smaller angle.

Find the size of each angle.

Calculate the size of angle x.

You must show all your working.

Eight identical sectors of a circle fit together to make a complete circle.

Calculate the value of x.

Calculate the size of angle x in the right-angled triangle shown below.

Diagram not drawn to scale

ABCD is a quadrilateral. BE is a straight line.

Calculate the size of angles a and b.

AB and CD are parallel.

Calculate the value of x.

Calculate the size of angle x in the right-angled triangle shown below.

Diagram not drawn to scale

ABCD is a quadrilateral. BE is a straight line.

Calculate the size of angles a and b.

AB and CD are parallel.

Calculate the value of x.

The sizes of angles a and b in the triangle shown below are in the ratio 2: 3.

Diagram not drawn to scale

Calculate the size of each of the angles a and b.

You must show all your working.

Show that the triangle below is not a right-angled triangle.

Diagram not drawn to scale

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The sizes of angles a and b in the triangle shown below are in the ratio 2: 3.

Diagram not drawn to scale

Calculate the size of each of the angles a and b. You must show all your working. [3 + 2 OCW]

Show that the triangle below is not a right-angled triangle.

Diagram not drawn to scale

C is a point on the straight line AB.

The straight line drawn at C makes two different angles above the line AB. One angle is twice the size of the other angle.

Calculate the size of each of the two angles.

The two angles are_{…........ ……} ° and_{…........ ……} °

PQ and RS are parallel.

Find the values of a, b and c.

Is it possible for an isosceles triangle to have an angle of 140°? Circle your answer.

You must give an explanation for your answer.

YES NO

Which of the following equations is correct for the diagram shown above?

Circle your answer.

a + b = 30 a + b = 210 b – a = 150

a – b = 150 a + b = 150

PQ and RS are parallel.

Find the values of a, b and c.

Is it possible for an isosceles triangle to have an angle of 140°? Circle your answer.

You must give an explanation for your answer.

YES NO

Is it possible for a rhombus to have an angle of 120° and an angle of 30°? Circle your answer.

You must give an explanation for your answer.

YES NO

In the diagram below, AB, BC and CD are three sides of a regular polygon.

The polygon has 15 sides. The length of each side is 8 cm. The exterior angle of the polygon is x°. BRC is a right-angled triangle.

Calculate the length of BR.

Calculate the value of x.

Calculate the size of angle x.

Hence, give the bearing of point B from point A.

Calculate the size of angle x.

Hence, give the bearing of point B from point A.

The exterior angle of a regular polygon is 36°.

How many sides does the polygon have?

Calculate the sum of all the interior angles of this regular polygon.

The exterior angle of a regular polygon is 36°.

How many sides does the polygon have?

Calculate the sum of all the interior angles of this regular polygon.

ABCD is a rectangle.

AB is parallel to EF. AC, CE and DG are straight lines.

Find the size of each of the angles a, b and c.

Measure BAC.

BAC =_........ °

One of the angles below is a reflex angle.

Circle the correct answer.

45° 90° 135° 180° 225°

The diagram below shows two angles on a straight line. The large angle is 5 times the size of the small angle.

Find the size of each angle.

ABCD is a rectangle.

AB is parallel to EF. AC, CE and DG are straight lines.

Find the size of each of the angles a, b and c.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A regular octagon with centre O is shown below.

Calculate the exact size of OAB. You may choose to draw additional lines on the diagram to help you.

You must show all your working.

In the following diagram, AE and BD are straight lines and BC = CE.

Is it possible to conclude that triangles ABC and DEC are congruent?

You must show all your working and explain your decision.

In the diagram below,

• ABCD is a square, • ADE is an equilateral triangle, • EAF is a straight line.

Calculate the size of angle x.

You must show all your working.

Line AB is parallel to line PQ.

Find the size of each of the angles a, b and c.

Find the size of each of the angles x and y.

Hence give the special name for triangle LMN.

The special name for triangle LMN is_........

Line AB is parallel to line PQ.

Find the size of each of the angles a, b and c.

Find the size of each of the angles x and y.

Hence give the special name for triangle LMN.

The special name for triangle LMN is_........

A, B and C are points on the circumference of a circle with centre O.

ACB = 74°.

Calculate the value of x. You must state any angle property of a circle that you use.

You must show all your working.

PS is a straight line.

Write down the size of angle x.

Find the size of angle y.

Circle the correct equation for each of the following.

All the lines shown are straight lines.

a + c + s + q = 360° p + a = 180° c = q d = r p + q + d + c = 180°

a b c d e 540 a b c d e 360

Calculate the size of angle x in the diagram below.

Circle the correct equation for each of the following.

All the lines shown are straight lines.

a = b + c
b = c + a
b = a − c
c = a + b
c = a – b

a b c d e 540 a b c d e 360

Circle the correct answer in each of the following.

Which of the following values cannot be an external angle of a regular polygon?

10° 18° 30° 48° 72°

Point A is on a bearing of 100° from point B.

What is the bearing of point B from point A?

260° 100° 280° 180° 80°

Calculate the size of angle x in the diagram below.

Circle the correct answer in each of the following.

Which of the following values cannot be an external angle of a regular polygon?

10° 18° 30° 48° 72°

Point A is on a bearing of 100° from point B.

What is the bearing of point B from point A?

260° 100° 280° 180° 80°

ABC is an isosceles triangle with AB = AC.

Calculate the value of y.

ABC is an isosceles triangle with AB = AC.

Calculate the value of y.

The line GH is a tangent to the circle at point Y.

The line EF is parallel to the line GH. The vertices of triangle EFY lie on the circle. EYG = 60°.

Prove that EFY is an equilateral triangle.

Give a reason for each step to justify your proof.

ABCD is a quadrilateral.

Calculate the value of x.

When ABCD is drawn to scale, would the lines AD and BC be parallel or not?

You must justify your answer without using a scale drawing.

ABCD is a quadrilateral.

Calculate the value of x.

When ABCD is drawn to scale, would the lines AD and BC be parallel or not?

You must justify your answer without using a scale drawing.

Circle either TRUE or FALSE for each of the following statements.

ABCDE is a regular pentagon with centre O.

Calculate the size of angle x.

You must show all your working.

Show that the triangle below is not a right-angled triangle.

Diagram not drawn to scale

A, B and C are points on the circumference of a circle.

XY is a tangent to the circle at the point A.

BAY = 74° and ABC = 53°. Prove that triangle ABC is an isosceles triangle. You must give a reason for any statement that you make or any calculation that you carry out.

Show that the triangle below is not a right-angled triangle.

Diagram not drawn to scale