Question

in which regular polygon is the measure of interior angle equal to the major of the exterior angle option a regular hexagon option B regular quadrilateral option C regular octagon option d regular decagon​

Answer 1

• Answer:

Hence, The measure of the Interior and Exterior Angles for each polygon are:

• (1) - REGULAR HEXAGON:

Interior Angle = 120 degrees

Exterior Angle = 60 degrees

• (2) - REGULAR QUADRILATERAL:

Interior Angle = 90 degrees

Exterior Angle = 90 degrees

• (3) - REGULAR OCTAGON:

Interior Angle = 135 degrees

Exterior Angle = 45 degrees

• (4) - REGULAR DECAGON:

Interior Angle = 144 degrees

Exterior Angle = 36 degrees

• Step-by-step explanation: SOLVE THE PROBLEM:

It seems like there are some typos in the problem statement. However, I believe you are asking for the measure of the interior angle and the measure of the exterior angle of a regular hexagon, quadrilateral, octagon, and decagon.

• Now, We solve these problems step by step:

• For a regular polygon with N sides, The formula for the measure of an interior angle is:

INTERIOR ANGLE = (N - 2) * 180 / N

• FORMULA for the measure of an EXTERIOR ANGLE:

EXTERIOR ANGLE = 360 / N

• (1) - REGULAR HEXAGON:

(N = 6)

• STEP (1) - Calculate the interior angle:

INTERIOR ANGLE = (6 - 2) * 180 / 6

• STEP (2) - SIMPLIFY:

INTERIOR ANGLE = 4 * 30

• STEP (3) - CALCULATE THE RESULT:

INTERIOR ANGLE = 120 degrees

• STEP (4) - CALCULATE THE EXTERIOR ANGLE:

EXTERIOR ANGLE = 360 / 6

• STEP (5) - SIMPLIFY:

EXTERIOR ANGLE = 60 degrees

• (2) - REGULAR QUADRILATERAL:

N = 4

• STEP (1) - CALCULATE THE INTERIOR ANGLE:

INTERIOR ANGLE = (4 - 2) * 180 / 4

• STEP (2) - SIMPLIFY:

INTERIOR ANGLE = 2 * 45

• STEP (3) - CALCULATE THE RESULT:

INTERIOR ANGLE = 90 degrees

• STEP (4) - CALCULATE THE EXTERIOR ANGLE:

EXTERIOR ANGLE = 360 / 4

• STEP (5) - SIMPLIFY:

EXTERIOR ANGLE = 90 degrees

• (3) - RGULAR OCTAGON:

N = 8

• STEP (1) - CALCULATE THE INTERIOR ANGLE:

INTERIOR ANGLE = (8 - 2) * 180 / 8

• STEP (2) - SIMPLIFY:

INTERIOR ANGLE = 6 * 22.5

• STEP (3) - CALCULATE THE RESULT:

INTERIOR ANGLE = 135 degrees

• STEP (4) - CALCULATE THE EXTERIOR ANGLE:

EXTERIOR ANGLE = 360 / 8

• STEP (5) - SIMPLIFY:

EXTERIOR ANGLE = 45 degrees

• (4) - REGULAR DECAGON:

N = 10

• STEP (1) - CALCULATE THE INTERIOR ANGLE:

INTERIOR ANGLE = (10 - 2) * 180 / 10

• STEP (2) - SIMPLIFY:

INTERIOR ANGLE = 8 * 18

• STEP (3) - CALCULATE THE RESULT:

INTERIOR ANGLE = 144 degrees

• STEP (4) - CALCULATE THE EXTERIOR ANGLE:

EXTERIOR ANGLE = 360 / 10

• STEP (5) - SIMPLIFY:

EXTERIOR ANGLE = 36 degrees

• STEP (6) - DRAW THE CONCLUSION:

Hence, The measure of the Interior and Exterior Angles for each polygon are:

• (1) - REGULAR HEXAGON:

Interior Angle = 120 degrees

Exterior Angle = 60 degrees

• (2) - REGULAR QUADRILATERAL:

Interior Angle = 90 degrees

Exterior Angle = 90 degrees

• (3) - REGULAR OCTAGON:

Interior Angle = 135 degrees

Exterior Angle = 45 degrees

• (4) - REGULAR DECAGON:

Interior Angle = 144 degrees

Exterior Angle = 36 degrees

I hope this helps you!