Given:
[tex]\angle A=5 x-12^{\circ}[/tex]
[tex]\angle B=2 x+24^\circ[/tex]
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
[tex]\Rightarrow 5 x-12^{\circ}=2 x+24^{\circ}[/tex]
Add 12° on both sides.
[tex]\Rightarrow 5 x-12^{\circ}+12^{\circ}=2 x+24^{\circ}+12^{\circ}[/tex]
[tex]\Rightarrow 5 x=2 x+36^{\circ}[/tex]
Subtract 2x from both sides.
[tex]\Rightarrow 5 x-2x=2 x+36^{\circ}-2x[/tex]
[tex]\Rightarrow 3x=36^{\circ}[/tex]
Divide by 3 on both sides.
[tex]$\Rightarrow\frac{3x}{3} =\frac{ 36^{\circ}}{3}[/tex]
⇒ x = 12°
Substitute x = 12° in ∠B.
m∠B = 2x + 24°
= 2(12°) + 24°
= 24° + 24°
= 48°
The measure of ∠B is 48°.
