Question

The measure of ∠1 is 150°. What are the measures of ∠4, ∠3 and ∠2?

Answer 1

∠1 is 150°

∠2 is 30°

∠3 is 150°

∠4 is 30°

Explanation:

∠1 is vertically opposite to ∠3 so they are equal

360° - (150° + 150°) = 360° - 300° = 60°

∠2 and ∠4 must sum to 60°

Answer 2

Explanation:

From the question

∠1 is opposite to ∠ 3 and vertically opposite angles are equal

So

∠1 = ∠ 3

That's

∠ 3 = 150°

∠ 3 and ∠ 4 are on a straight line and angles on a straight line add up to 180°

So to find ∠4, subtract ∠3 from 180°

That's

∠ 4 = 180 - ∠ 3

∠ 4 = 180 - 150

∠ 4 = 30°

Since ∠ 4 and ∠ 2 are opposite they are also equal

That's

∠ 4 = ∠ 2

Therefore

∠ 2 = 30°

Hope this helps you