Angles in Polygons & Parallel Lines Practice Questions

Work out the size of each exterior angle of a regular polygon with $15$ sides.

Work out the size of each interior angle of a regular polygon with $15$ sides.

Each interior angle of a different regular polygon is $165^\circ$.

Work out the number of sides of this polygon.

Write down the size of the angle marked $x$.

Give a reason for your answer.

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

Give a reason for your answer.

Work out the value of $y$.

Work out the size of angle $BOD$.

Give a reason for your answer.

$ABCDEF$ is a hexagon. The table shows the sizes of its six interior angles.

Interior angle	$FAB$	$ABC$	$BCD$	$CDE$	$DEF$	$EFA$
Size	$147^\circ$	$105^\circ$	$130^\circ$	$x$	$98^\circ$	$2x$

Work out the size of the largest interior angle of the hexagon.

You must show all your working.

Write down the size of angle $ACB$.

Give a reason for your answer.

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

Give a reason for each stage of your working.

Work out the size of each interior angle of a regular pentagon.

Work out the size of each interior angle of polygon $P$.

Work out the number of sides of polygon $P$.

Diagram NOT accurately drawn.

$ABCDE$ is a regular pentagon. $AD$ is a diagonal of the pentagon.

Prove that $AD$ is parallel to $BC$.

You must give a reason for each stage of your working.

Polygon $A$ is a regular polygon with $n$ sides.

Polygon $B$ is a regular polygon with $2n$ sides.

Each interior angle of polygon $B$ is $12^\circ$ greater than each interior angle of polygon $A$.

Work out the value of $n$.