Angle facts

MN is a straight line.

Work out the value of x.

A, C and D are points on a circle, diameter AC. ABC is an isosceles triangle with AC = BC BCD is a straight line.

Work out the size of angle x.

A straight line is drawn across a regular octagon.

Work out the size of angle x.

x = °

Lines AB, BC, CD and AD form two triangles.

Work out the length of AD.

AB is a straight line.

Work out the size of angle x.

Work out the size of angle y.

Three straight lines intersect as shown.

What type of triangle is made? You must show your working.

AB and CD are straight, parallel lines. P is a point on AB. Q is a point on CD. AP = AQ

Work out the value of x.

AB is a straight line. Both angles are given in degrees.

By working out the value of x, work out the ratio smaller angle: larger angle

AB is a straight line.

Is y half of x ? Tick a box.

Show working to support your answer.

b = 45 ° and a: b = 7: 3 and x: y = 4: 1

Show that a: y = 5: 2

Work out the size of an exterior angle of a regular hexagon.

AF, BC, DE and DF are straight lines. BC and DE are parallel.

p is three times r.

Work out the size of angle p.

AF, BC, DE and DF are straight lines. BC and DE are parallel.

p is three times r.

Work out the size of angle p.

AC is a diameter of a circle, centre E. E is the midpoint of BD.

Prove that triangle ABE is congruent to triangle CDE.

Work out the area of triangle ABC.

ABC, BD and BE are straight lines.

angle EBD = 5 × angle ABE angle DBC = 3 × angle ABE Work out the size of angle EBD.

ABC, BD and BE are straight lines.

angle EBD = 5 × angle ABE angle DBC = 3 × angle ABE Work out the size of angle EBD.

19

Assume that the polygon is an octagon. Work out the size of angle x.

In fact, the polygon has more sides than an octagon. What does this mean about the size of angle x ? Tick one box.

6

Assume that the polygon is an octagon. Work out the size of an exterior angle.

In fact, the polygon has more sides than an octagon. What does this mean about the size of an exterior angle? Tick one box.

For each statement, tick the correct box.

Two angles around a point are shown.

The angles are in the ratio 2: 7 Show that the larger angle is 280 °

Here are three straight lines.

Are the lines AB and CD parallel? Tick a box.

Show working to support your answer.

P, Q and R are points on a circle. SP is a tangent to the circle.

Prove that y = 90 ° – x

Some people were asked for the main way they listen to music. A pie chart is drawn to represent their answers.

Work out the size of angle x.

135 people said Computer. How many people said Phone?

Write down the size of angle w.

Work out the size of angle x.

In a triangle, two of the angles are 51 ° and 74 °. Work out the size of the third angle.

Here is a triangle.

Give your answer as a fraction in its simplest form.

Here is a different triangle.

x = 3 y Work out the size of angle y.

y = °

AB, BC and CD are sides of a regular 12-sided polygon. CDMN is a square.

Prove that points A, B and N lie on a straight line.

Shapes X and Y are shown on a centimetre grid.

Circle the name of shape X.

pentagon hexagon octagon decagon

Give a reason why shape Y is not a regular polygon.

Complete these statements.

Circle the pair of alternate angles.

a and b b and c c and d a and d

One side of a triangle is extended.

Circle the size of angle x.

100 ° 80 ° 60 ° 40 °

A straight line passes through two parallel lines.

Circle the angle that is corresponding to angle x.

a b c d

AB is parallel to CD. FG is a straight line.

Work out the size of angle x.

Lines A, B, C, D and E intersect as shown. Lines A and B are parallel.

Work out the size of angle x.

Part of a regular polygon with 15 sides is shown.

Work out the size of an interior angle.

Part of a regular polygon with 15 sides is shown.

Work out the size of an interior angle.

Circle the size of angle x.

70 ° 110 ° 250 ° 270 °

AB, BC, CD and DE are four of the sides of a regular decagon.

Work out the size of angle w.

AB is a straight line.

Work out the size of angle x.

ADB and CD are straight lines.

angle ADC = 5 × angle CDB Work out the size of angle ADC.

J and K are ships. P is a port. J is due South of P. Angle JPK = 56°

Work out the bearing of J from K.

J and K are ships. P is a port. J is due South of P. Angle JPK = 56°

Work out the bearing of J from K.

The interior angle of a regular pentagon is 108° Work out the sum of the five reflex angles at the vertices of a regular pentagon.

Omar asks Harry,

“How many lines of symmetry does a pentagon have?” Harry assumes it is a regular pentagon. His answer is 5.

Draw the lines of symmetry on this regular pentagon.

Omar then says, “What if the pentagon is not regular?” For a pentagon that is not regular, what is true about the number of lines of symmetry? Tick one box.

In rectangle ABCD triangle ABE is equilateral triangle CDE is isosceles, with CE = DE

Work out the size of angle x.

The sum of the angles in any quadrilateral is 360° For example, in a rectangle 4 × 90° = 360° Zak writes, 5 × 90° = 450° so the sum of the angles in any pentagon must be 450° Is he correct?

Show working to support your answer.

The sum of the angles in any quadrilateral is 360° For example, in a rectangle 4 × 90° = 360° Zak writes, 5 × 90° = 450° so the sum of the angles in any pentagon must be 450° Is he correct?

Show working to support your answer.

BCD is a straight line. Triangle ABC is equilateral. CE = DE

Work out the size of angle x.

Amba is working out the size of an interior angle of a regular octagon.

Her method is Interior angle = 360 ÷ 8 Is her method correct?

Give a reason for your answer.

What is the size of an exterior angle of a regular decagon? Circle your answer.

18° 36° 144° 162°

ABCD is a quadrilateral. Sides are extended as shown.

Show that x = 100°

Two congruent regular polygons are joined together.

Work out the number of sides on each polygon.

A regular polygon has an exterior angle of 20° Work out the number of sides of the polygon.

Is BCD a straight line? Show working to support your answer.

AB, CD and EF are straight lines.

Ava assumes that AB and CD are parallel. What answer should she get for the size of angle y ?

In fact, AB and CD are not parallel angle w is 60° What effect does this have on the size of angle y ? Tick a box.

Show working to support your answer.

AB, CD and EF are straight lines.

Ava assumes that AB and CD are parallel. What answer should she get for the size of angle y ?

In fact, AB and CD are not parallel angle w is 60° What effect does this have on the size of angle y ? Tick a box.

Show working to support your answer.