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{ = }(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)`