Question

Transversal c intersects lines a and b. Prove that a||b in each case. Given that m∠3 = 45° and m∠5 = 3 ⋅ m∠3, what's the measure of angle 5?

a) 45°
b) 54°
c) 117°
d) 126°

Answer 1

To prove that lines a and b are parallel, we need to show that the corresponding angles formed by the transversal c are congruent. Given that m∠3 = 45° and m∠5 = 3 ⋅ m∠3, we can substitute the value of m∠3 into the equation for m∠5 to find that angle 5 measures 135°.

Step-by-step explanation:

In order to prove that lines a and b are parallel, we need to show that the corresponding angles formed by the transversal c are congruent.

Given that m∠3 = 45° and m∠5 = 3 ⋅ m∠3, we can substitute the value of m∠3 into the equation for m∠5:

m∠5 = 3 ⋅ 45° = 135°

Therefore, the measure of angle 5 is 135°.