Question

A regular decagon with exterior angle 1 is shown.

In the regular decagon shown, what is the measure of angle 1?

°

Answer 1

Answer: 36°

Step-by-step explanation: Trust Me!

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In the regular decagon shown, what is the measure of angle 1?

• 36°

360° is always the sum of all measures of all exterior angles of a convex polygon. A decagon have 10 sides.

Since ∠1 = 36°, then each other angle should measure the same, 36°.

In order to know whether the sum of all the angles equal 360°,
we need to multiply: 36° x 10.

36° x 10= 360°.

And sure enough the answer is correct.

Answer 2

∠1 = 36°

Explanation:

All angles of a regular polygon are congruent, as are the sides. A regular decagon will have 10 congruent angles.

Exterior angles

The sum of the measures of the exterior angles of a convex polygon is always 360°. This decagon has 10 congruent exterior angles, so the measure of each is given by ...

10(∠1) = 360°

∠1 = 36° . . . . . . . . divide by 10