Question

Transversal t cuts parallel lines a and b as shown in the diagram. Which equation is necessarily true?

A. m∠1 = m∠2

B. m∠4 = m∠6

C. m∠1 + m∠5 = 90°

D. m∠3 + m∠5 = 180°

E. m∠7 = m∠8

Answer 1

Sum of Interior Angles Same Side of Transversal equals 180.

That means

m∠3+m∠5 = 180⁰

Answer is D.

Answer 2

Option D; m∠3 + m∠5 = 180°

This is about angle theorems.

• Option A: m∠1 = m∠2. This is not true because sum of angles on a straight line is 180° and the line that divides this 2 angles is not perpendicular to the straight horizontal line to bisect it equally.

• Option B: m∠4 = m∠6; This statement is not true because though their sum is 180° but again they are transverse angles which are not equal from the line that forms them.

• Option C: m∠1 + m∠5 = 90°; This is not correct because m∠1 = m∠5 and the line that forms each of them is not a 45° angle

• Option D; m∠3 + m∠5 = 180°. This is true because from angle from the same side of the transversal theorem, they must add up to 180°.

• Option E; m∠7 = m∠8. Same reason as in option A, the statement is not true

That means only option D is true.

Read more at; brainly.com/question/12915942