Study guides

☆☆

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

Write your answer...

Submit

Still have questions?

Continue Learning about Other Math

No, they are supplementary, not complementary.

AnswerIt is Dodecagon.To find this, you have to first find the exterior angle of the polygon. Since the exterior angle of a polygon is always supplementary to the interior angle, you subtract the measure of the interior angle from 180. 180-150=30. Now You divide 360 by the measure of the exterior angle to get the number of sides of the polygon. 360/30=12. A 12-sided polygon is called a dodecagon

180-interior angle = exterior angle 360/exterior angle = number of sides

144o. Sum of exterior angles of a polygon is 360o. Each exterior angle for a regular decagon is 360o / 10 = 36o. Exterior and interior angles are supplementary, that is sum to 180o. Therefore the interior angle of a regular decagon is 180o - 36o = 144o.

Interior angle + Exterior angle = 180 So Interior angle = 180 - Exterior angle Interior angle = 4*Exterior angle + 30 Substitute for Interior angle: 180 - Exterior angle = 4*Exterior angle + 30 Collect like terms: 150 = 5*Exterior angle Divide by 5: Exterior angle = 30 deg Therefore number of sides = 360/30 = 12

Related questions

The interior angle of a polygon and its adjacent exterior angle can never be complementary.

Ah...

An interior or exterior angle of the polygon.

No, they are supplementary, not complementary.

In a polygon there are no such angles.

equal to 180°

No. The interior angle and exterior angle at the same vertex are supplementary. Each of them is (180 degrees minus the other). In rectangles (including squares), the interior and exterior angles at each vertex are both right angles.

The sum of an adjacent interior and its exterior angle will total to 360°. If the angles were to be equal, they would both have to be 180°. An angle of 180° is a straight line. A polygon may be composed of straight lines that intersect at vertices but a straight line has no vertex. That being the case, the answer to your question is "No".

Measure them with a protractor

With a protractor or if you know the exterior angle then it's 180 - exterior angle = interior angle

It is: 180-exterior angle = interior angle because there are 180 degrees on a straight line

Interior angles are angles formed by two adjacent sides on the inside of a polygon. An exterior angle is the supplement of the interior angle.

People also asked