Question

The measure of ∠4 is 34°. What are the measures of ∠1, ∠2, and ∠3, respectively?

A. ∠1 = 146°, ∠2 = 146°, ∠3 = 34°
B. ∠1 = 146°, ∠2 = 34°, ∠3 = 146°
C. ∠1 = 124°, ∠2 = 34°, ∠3 = 124°
D. ∠1 = 34° , ∠2 = 146°, ∠3 = 34°

DONT PUT NONSENSE ANSWERS

Answer 1

B) <1 = 146, <2 = 34, <3 = 146

Explanation:

Because measure angle 4 is 34°

And the angle opposite of <4 is <2 and they’re both congruent so <4 = <2. Therefore, <2 = 34.

By finding <1 and <3 is simply finding a supplementary angle because:

<4 + <1 = 180°

<4 + <3 = 180°

So,

34 + <1 = 180°

<1 = 146°

and,

34 + <3 = 180°

<3 = 146

Answer 2

B

Explanation:

∠4 and ∠2 are vertical angles

Vertical angles are congruent

Which means that because ∠4 = 34°, ∠2 also = 34°

∠1 and ∠4 are supplementary angles.

Supplementary angles add up to equal 180

Which means that ∠1 + ∠4 = 180

or ∠1 + 34° = 180

subtract 34 from each side

180 - 34 = 146

Hence, ∠1 = 146

∠1 and ∠3 are vertical angles

Like stated before vertical angles are congruent

Which means that because ∠1 = 146°, ∠3 also = 146

So we can conclude that the answer is B