Question

ABCDEFGHIJ is a regular decagon and the measure of <D is 144º. What is the measure of <A?

A) 90°
B) 100°
C) 144°
D 220°

ABC is an equilateral triangle and the measure of <A is 60°. What is the measure of <C?

A) 45°
B) 60°
C) 90°
D) 180°​

Answer 1

given ABCDEFGHIJ is a decagon

As we know the sum of all ten interior angles of a decagon = 1440°

so measure of each angle of decagon = (1440/10)° = 144°

so the measure of ∠A would be 144° (C)

given Δ ABC is a equilateral triangle

As we know the sum of all three interior angles of a equialter traingle = 180°

so if one angle of an equilateral triangle is 60°

then the remaining of the angles would have the measure of 60° each

So answer = 60°(B)

Hope it helps

Answer 2

1. 144⁰

2. 60⁰

Explanation:

The formula to find the measure of the interior angles of a regular polygon is:

m< = (n - 2) • 180/n where n = the number of sides

For a decagon, there are 10 sides.

m< = (10-2) • 180/10 = 144°

A regular polygon/equilateral triangle is defined as having equal sides and angles.