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Shaylittickley
Answered

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

Verified Answer :

calculista

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

\(y=180-60=120\)°

\(x eq y\)

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



JeanaShupp

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°

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