Question

∠A and \angle B∠B are supplementary angles. If m\angle A=(3x-17)^{\circ}∠A=(3x−17)

Answer 1

The measure of angle B is 65°

Explanation:

Given that ∠A and ∠B are supplementary angles.

The measures are ∠A = (3x - 17)° and ∠B = (2x-23)°

The value of x:

Since, supplementary angles add up to 180°, then we have,

$\angle A+ \angle B=180^{\circ}$

Substituting the values, we have,

$3x-17+2x-23=180$

               $5x-40=180$

                       $5x=220$

                        $x=44$

Thus, the value of x is 44

Measure of angle B:

Let us determine the measure of angle B by substituting the value of x in ∠B = (2x-23)°

Thus, we have,

$\angle B=(2(44)-23)^{\circ}$

$\angle B=(88-23)^{\circ}$

$\angle B=65^{\circ}$

Thus, the measure of angle B is 65°