Angles in Polygons & Parallel Lines (CIE IGCSE Maths: Extended)

The diagram shows two triangles,  and .

 is a straight line, , angle  and angle .
Work out angle .

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

Find the number of sides of a regular polygon with interior angle 162°.

The interior angle of a regular polygon with sides is .

Work out the value of .

................................................

The diagram shows triangle ABC.
The triangle is reflected in the line BC to give a quadrilateral ABDC.

Write down the mathematical name of the quadrilateral ABDC.

Find angle ACD.
 

Angle ACD = ................................................

and  is a straight line.
 
Find the value of .
 

.................................................

The exterior angle of a regular polygon is ° and the interior angle is °.

Calculate the number of sides of the polygon.

Complete the statements.

a = ............................................... because ...............................................     
b = ............................................... because ...............................................     

The diagram shows a regular octagon and a regular hexagon.

Find the size of the angle marked .
You must show all your working.

ABDF is a parallelogram and BCDE  is a straight line.
AF = 12cm, AB = 9 cm, angle CFD = 40° and angle FDE = 80°.

Explain why triangle CDF  is isosceles. 

PQR is a triangle.
T is a point on PR and U is a point on PQ.
RQ is parallel to TU.

Explain why triangle PQR is similar to triangle PUT.
Give a reason for each statement you make.

The diagram shows a trapezium.

Work out the value of .

..................................................

A hexagon has five angles that each measure 115°.

Calculate the size of the sixth angle.

The angles of a quadrilateral are , , and .

Find the value of .

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

The diagram shows an isosceles triangle ABC with AB = AC.
LCM and BCN are straight lines and LCM is parallel to AB.
Angle ACL = 56°.
 
Find the value of  and the value of .
 

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

The diagram shows a regular pentagon.
and  are two of the lines of symmetry of the pentagon.

Work out the size of the angle marked .
You must show all your working.

 is a regular 9-sided polygon.

The vertices  and  are joined with a straight line.

Work out the size of angle .
You must show how you get your answer.

 is a regular pentagon.
and  are points on a circle, centre .
and  are tangents to the circle.
 is a straight line.

Prove that .