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,
[tex]\angle A+ \angle B=180^{\circ}[/tex]
Substituting the values, we have,
[tex]3x-17+2x-23=180[/tex]
[tex]5x-40=180[/tex]
[tex]5x=220[/tex]
[tex]x=44[/tex]
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,
[tex]\angle B=(2(44)-23)^{\circ}[/tex]
[tex]\angle B=(88-23)^{\circ}[/tex]
[tex]\angle B=65^{\circ}[/tex]
Thus, the measure of angle B is 65°
