Question

An exterior angle of a regular polygon measures 45 degrees. What is the measure of an interior angle?

135 degrees
145 degrees
45 degrees

Answer 1

The exterior angle of a polygon and its corresponding interior angle always add up to 180°.

Let the interior angle of the polygon be
`y^(\circ)`

`45^(\circ)+y=180^(\circ)`

So,
`y=180^(\circ)-45^(\circ)`

`y=135^(\circ)`

So, the interior angle of the polygon is
`135^(\circ)`