Question

Angle P is 3 more than twice angle M. Find the measure of the 2 angles if they are supplementary.

Answer 1

$\angle P\text{ = 2}\angle M\text{ + 3}$

Since Angle P and Angle M are supplementary angles, two angles are supplementary if the sum of their measures is equaled 180 degrees. Thus, we make this equation,

$\angle P\text{ + }\angle M=180^{\circ}$

Substituting the proportional relationship of Angle P to Angle M,

$\angle P\text{ + }\angle M=180^{\circ}\text{ ; (2}\angle M\text{ + 3) + }\angle M=180^{\circ}$$3\angle M=180-3=177^{\circ}$$\angle M\text{ = }\frac{177^{\circ}}{3}=59^{\circ}$

Since we now have the measure of Angle M, let's now find the measure of Angle P,

$\angle P\text{ + }\angle M=180^{\circ}$$\angle P+59^{\circ}=180^{\circ}$$\angle P=180^{\circ}-59^{\circ}=121^{\circ}$