Given:
∠A and ∠B are supplementary angles.
m∠A=(x−18)° and m∠B=(x−20)°.
To find:
The measure of ∠B.
Solution:
Sum of supplementary angles is always 180 degrees.
∠A and ∠B are supplementary angles. So,
[tex]m\angle A+m\angle B=180^\circ[/tex]
[tex](x-18)^\circ+(x-20)^\circ=180^\circ[/tex]
[tex](2x-38)^\circ=180^\circ[/tex]
[tex]2x-38=180[/tex]
Now,
[tex]2x=180+38[/tex]
[tex]2x=218[/tex]
[tex]x=\dfrac{218}{2}[/tex]
[tex]x=109[/tex]
The measure of angle B is
[tex]m\angle B=(x-20)^\circ[/tex]
[tex]m\angle B=(109-20)^\circ[/tex]
[tex]m\angle B=89^\circ[/tex]
Therefore, the measure of ∠B is 89°.
