Question

Given the regular polygon, what is the measure of each numbered angle?

A. m∆ 1 = 12°; m ∆ 2 = 72°
B. m ∆ 1 = 12°; m ∆ 2 = 144°
C. m ∆ 1 = 36°; m ∆ 2 = 72°
D. m ∆ 1 = 36°; m ∆ 2 = 144°​

Answer 1

Explanation:

n = 10

m∠1 = 360°/ n

= 360°/10

= 36°

`2 × m∠2 = ((n - 2)180)/(n) \\ = ((10 - 2)180)/(10) \\ = (8 * 180)/(10) \\ = 8 * 18 \\ 2 × m∠2 = 144° \\ m∠2 = 72°`

I would correct my answer

#CMIIW

Answer 2

• C. m∠1 = 36°; m∠2 = 72°

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Given is a regular decagon.

It has 10 congruent sides and each angle opposite to sides is congruent to ∠1.

To find its measure divide 360° by the number of sides (angles):

• m∠1 = 360°/10 = 36°

Angle 1 is formed by two diagonals. Since all diagonals are of same length, the triangle formed by the diagonals and a side is isosceles.

It means there are two of ∠2 and one ∠1 in each triangle.

We know the measure of ∠1, now use the triangle sum property to find the measure of ∠2:

• 2 × m∠2 + m∠1 = 180°
• 2 × m∠2 + 36° = 180°
• 2 × m∠2 = 144°
• m∠2 = 72°

The matching choice is C