Question

What is the measure of arc EA?

A. 21
B. 36
C. 30
D. 51

Answer 1

Based off the measures of the arcs DC and AB, your answer should be B. 36 Hope it helps.

Answer 2

The correct option is C. 30°

Explanation:

Construction : Join OB and OA

Now, m∠ECB = 51°

Now, ∠ECB and ∠EOA are formed on the same base

⇒ m∠EOA = 2 × m∠ECB

⇒ m∠EOA = 2 × 51°

⇒ m∠EOA = 102°

Now, Angle in the arc = Angle formed by the arc at the center

⇒ m∠AOB = measure of arc AB

⇒ m∠AOB = 72°

Now, m∠EOA = 102° - 72°

⇒ m∠EOA = 30°

Since, Angle in the arc = Angle formed by the arc at the center

⇒ Measure of arc EA = measure of the angle EOA

⇒ Measure of arc EA = 30°

Therefore, The correct option is C. 30°