Angles in Polygons & Parallel Lines (Cambridge O Level Maths)

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 .

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

The diagram shows a hexagon.

Write an equation and solve it to 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.

 is a parallelogram.

Angle .
Angle .
Angle .

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

For the triangle, show that  .

[1]

For the quadrilateral, show that  .

[1]

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

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

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 .

and  are straight lines.

The diagram shows a regular 10-sided polygon,

Show that .