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

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 diagram shows two parallel lines PAQ and SBCT.

AB = AC and angle QAC = 43°.

Find the value of .

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

Complete the statements.

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

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

Find angle .
 

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

The area of pentagon is .
The area of pentagon is .

Find the ratio    perimeter of pentagon : perimeter of pentagon     in its simplest form.
 

......................... : .........................

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 .
 

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

 is a parallelogram.

Angle .
Angle .
Angle .

Calculate the size of angle .
You must give reasons for your answer.