Angles in Polygons & Parallel Lines (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

The interior angle of a regular polygon with  sides is 150°.  

Calculate the value of .  

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

A regular polygon has 72 sides.

Find the size of an interior angle.

The diagram shows two parallel lines PAQ and SBCT.

AB = AC and angle QAC = 43°.

Find the value of .

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

is parallel to , is an isosceles triangle and is a straight line.

Find the value of .   

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

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.  

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

In a regular polygon, the interior angle is 11 times the exterior angle.

i) Work out the number of sides of this polygon.

[3]

ii) Find the sum of the interior angles of this polygon.

[2]

 is a parallelogram.

Angle .
Angle .
Angle .

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

The diagram shows a triangle and a quadrilateral. All angles are in degrees.

i) For the triangle, show that  .

[1]

ii) For the quadrilateral, show that  .

[1]

iii) Solve these simultaneous equations.
Show all your working.

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

= ................................................... [3]

iv) Find the size of the smallest angle in the triangle.

[1]

Show that each interior angle of a regular pentagon is . 

The diagram shows a regular pentagon .
The vertices of the pentagon lie on a circle, centre , radius .
is the midpoint of .

i) Find .  

= ........................................ cm [3]

and  are straight lines.

iia) Find .   

= ........................................ cm [3]

iib) Calculate the area of triangle .   

........................................ cm² [3]

The diagram shows a regular 10-sided polygon,

Show that .