Question

Determine if the statement is always, sometimes or never true.
The measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle.


always

sometimes

never

Answer 1

Let

x--------> the measure of the adjacent interior angle

y--------> the measure of an exterior angle at the vertex of a polygon

we know that

The measure of the adjacent interior angle and the measure of an exterior angle at the vertex of a polygon are supplementary angles

so

$x+y=180$°

Examples

case 1)

In a square

$x=90$°

so

$y=180-90=90$°

$x=y$

In this case

The measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle

case 2)

an equilateral triangle

$x=60$°

so

$y=180-60=120$°

$x\neq y$

In this case

The measure of an exterior angle at the vertex of a polygon is not equals the measure of the adjacent interior angle

therefore

the answer is

sometimes

Answer 2

Answer: Sometimes

Step-by-step explanation:

Only rectangle and square are the polygons in which measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle because each has angle is right angle.

such that the exterior angle =  180°-90°=90°

Rest of the polygons does not satisfy the statement that the measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle.

Since in equilateral triangle each angle is of 60°, that is the measure of exterior angle = 180°-60°=120°