Question

I need the answer asap

Answer 1

Given:

$\angle A=5 x-18^{\circ}$

$\angle B=3 x+42^{\circ}$

To find:

The value of x and measure of angle A

Solution:

Alternate interior angle theorem:

If two parallel lines cut by a transversal, then the alternate interior angles are congruent.

⇒ m∠A = m∠B

$5x-18^\circ=3x+42^\circ$

Add 18° on both sides.

$5x-18^\circ+18^\circ=3x+42^\circ+18^\circ$

$5x=3x+60^\circ$

Subtract 3x from both sides.

$5x-3x=3x+60^\circ-3x$

$2x=60^\circ$

Divide by 2 on both sides.

⇒ x = 30°

Substitute x = 30° in ∠A.

m∠A = 5x - 18°

       = 5(30°) - 18°

       = 150° - 18°

       = 132°

The measure of ∠A is 132°.