Angles in Polygons & Parallel Lines (AQA GCSE Maths: Foundation): Exam Questions

The diagram shows an isosceles triangle and a straight line.
Work out the value of .

...............................[2]

Work out the value of
Give reasons for your answer.

............................ because ....................................................................................................

is an isosceles triangle and is a straight line.

Find the value of .

= ................................................... 

is an isosceles triangle.
is a straight line.

Find the value of .

= .............................................. 

is a straight line and is an isosceles triangle.
Find the value of.

= ................................................. 

In the triangle and angle .

is a straight line.

Work out angle .

Angle = .................................................. 

A triangle is isosceles.
One of its angles is 96°.

Find the other two angles.

........................ and ........................ 

Find the value of .

= ................................................... 

The diagram shows a triangle drawn between a pair of parallel lines.

Find the value of and the value of .

A regular polygon has an exterior angle of 20°.

Work out the number of sides of this polygon.

The diagram shows two parallel lines and two straight lines.

i) Find the value of .

Give a reason for your answer.

a = ................ because ..................................................................................................... [2]

ii) Find the value of .
Give a reason for your answer.

b = ................ because ......................................................................................................[2]

iii) Find the value of .

= ................................................. [2]

In the diagram, is parallel to .

Find the value of.
Give a geometrical reason for your answer.

= ......................... because ....................................

Work out the value of .
Give a geometrical reason for your answer.

.................because ......................

Work out the value of

i)

=..........................[1]

ii)

...........................[1]

The diagram shows a triangle between two parallel lines, and .

Find the value of

i)

=............................. [1]

ii)

............................. [1]

iii) .

= .............................  [1]

Complete the statements.

............................ because ............................   

........................... because ............................ 

The diagram shows a trapezium.

Work out the value of .

= ..................................................

Kim knows that one angle of an isosceles triangle is 48°.
He says that one of the other angles must be 66°.

Explain why Kim is wrong.

The diagram shows triangle and a straight line . is a point on .
Angle = 25°, angle = 32° and .

i) Find angle

Angle = ................................................... [2]

ii) Find angle .

Angle = ................................................... [2]

The diagram shows a triangle.

Use the diagram to write down an equation and solve it to find the value of .

 = .................................. [4]

The diagram shows an isosceles triangle, .
is a straight line.

Find the value of .

................................ [2]

is a rectangle.
is parallel to .

Find the value of and the value of .

= ......................................................
= ................................................. .....

Two regular octagons and a square meet at point .
Show, by calculation, that the three interior angles at add up to 360°.

The diagram shows two pairs of parallel lines.

Find the value of , the value of and the value of .

The diagram shows part of a different regular polygon.

is an exterior angle.
is an interior angle.
The ratio .

i) Work out angle .

[3]

ii) Work out the number of sides of this regular polygon.

[1]

is a pentagon.

Explain why the diagram shows that the sum of the interior angles of a pentagon is 540°.
Do not measure any angles.

In the diagram and are straight lines.
Lines and are parallel.

Find angle and give a reason for your answer.

Angle = ................................. because ...................................

The diagram shows two regular pentagons.
Pentagon  is an enlargement of pentagon , centre .

Find angle .

Angle  = .............................. 

In the diagram,  is a straight line. is parallel to , angle  = 34° and 

i) Complete the statements.

a) ................ because ................................

[2]

b) ................ because .................................

[2]

ii) Work out the value of and the value of .

....................   
  .................... [2]

iii) Find the value of t and give a reason for your answer.

................ because ........................

[2]

Each interior angle of a regular polygon is 162°.

Calculate the number of sides of the polygon.