Angles in Polygons & Parallel Lines Practice Questions

Work out the size of the angle marked $x$.

Two straight lines cross as shown.

Write down the size of the angle marked $y$.
Give a reason for your answer.

Work out the sum of the interior angles of a decagon.

A regular decagon has 10 equal interior angles.

Work out the size of one interior angle of a regular decagon.

Write down the size of one exterior angle of a regular decagon.

$PQ$ is a straight line.

Work out the size of the angle marked $x$.

In triangle $ABC$, $AB = AC$ and angle $BAC = 34^\circ$.

Work out the size of the angle marked $x$.

Write down the letter of the angle that is alternate to the angle of $48^\circ$.
Write down the size of this angle.

Write down the letter of the angle that is co-interior (allied) with the angle of $48^\circ$.
Work out the size of this angle.
Give a reason for your answer.

Work out the value of $x$.
You must show all your working.

Write down the size of the largest angle of the quadrilateral.

Show that the sum of the interior angles of a hexagon is $720^\circ$.

Work out the size of the angle marked $x$.

The exterior angle of a regular polygon is $15^\circ$.

Work out the number of sides of the polygon.

The interior angle of a different regular polygon is $162^\circ$.

Work out the number of sides of this polygon.

Show that angle $QPR = 68^\circ$.
Give a reason for each stage of your working.

Explain why $3x + 12 = 5x - 20$.

Work out the size of the angle marked $(3x + 12)^\circ$.
You must show all your working.

Work out the size of angle $x$.
Give a reason for each stage of your working.

Work out the value of $n$.
You must show all your working.

Is Jordan correct?
You must show how you get your answer.