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den301095 [7]
3 years ago
7

Determine if the statement is always, sometimes or never true.

Mathematics
2 answers:
NNADVOKAT [17]3 years ago
8 0

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°

Romashka-Z-Leto [24]3 years ago
4 0

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°

<u>Examples</u>

case 1)

<u>In a square</u>

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)

<u>an equilateral triangle</u>

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

<u>the answer is</u>

sometimes



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