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°.