In the figure, m∥n. Given that m∠3 =(4x−7)° and m∠5 =(6x−81)°, what is the measure of ∠8?

m∠8 = 39°

Step-by-step explanation:

Given:

m∠3 = (4x−7)°

m∠5 = (6x−81)°

Required:

m∠8?

Solution:

First, find the value of x.

Since, line m is parallel to line n, therefore,

m∠3 = m∠5 (alternate interior angles are congruent)

(substitution)

Collect like terms

Divide both sides by -2

Find m∠8:

m∠8 + m∠5 = 180° (linear pair)

m∠8 + (6x - 81)° = 180° (substitution)

Plug in the value of x

m∠8 + (6(37) - 81)° = 180°

m∠8 + (222 - 81)° = 180°

m∠8 + 141° = 180°

Subtract 141 from both sides

m∠8 = 180° - 141°

m∠8 = 39°

3030 ur welcome

step-by-step explanation: