Question

The angle measurements in the diagram are represented by the following expressions.

Answer 1

Given:

`\angle A=5 x-12^(\circ)`

`\angle B=2 x+24^\circ`

To find:

The value of x and measure of angle B

Solution:

Alternate interior angle theorem:

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

⇒ m∠A = m∠B

`\Rightarrow 5 x-12^(\circ)=2 x+24^(\circ)`

Add 12° on both sides.

`\Rightarrow 5 x-12^(\circ)+12^(\circ)=2 x+24^(\circ)+12^(\circ)`

`\Rightarrow 5 x=2 x+36^(\circ)`

Subtract 2x from both sides.

`\Rightarrow 5 x-2x=2 x+36^(\circ)-2x`

`\Rightarrow 3x=36^(\circ)`

Divide by 3 on both sides.

`$\Rightarrow(3x)/(3) =( 36^(\circ))/(3)`

⇒ x = 12°

Substitute x = 12° in ∠B.

m∠B = 2x + 24°

= 2(12°) + 24°

= 24° + 24°

= 48°

The measure of ∠B is 48°.