MHB Complementary & Supplementary Angles

[bernardl]

The m<P is three less than twice the measure of <Q. If <P and <Q are supplementary angles, find the measures of both angles.
The m<B is two more than three times the measure of <C. If <B and <C are complementary angles, find the measures of both angles.

 

[Greg]

Hello! :D

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[bernardl]

I honestly don't know how to do both of those questions!

 

[Greg]

O.k., let's try the first one. mP + mQ = 180 degrees. mP = 2mQ - 3. Make sense? Can you solve it now?

 

[HallsofIvy]

"The m<P is three less than twice the measure of <Q. If <P and <Q are supplementary angles, find the measures of both angles."
Do you know that "supplementary angles" means their measures sum to 180 degrees? m<P+ m<Q= 180. You are also told that m<P= 2m<Q- 3 so (2m<Q- 3)+ m<Q= 3m<Q- 3= 180. Solve that for m<Q then use m<P+ m<Q= 180 to find m<P "The m<B is two more than three times the measure of <C. If <B and <C are complementary angles, find the measures of both angles."

"Complementary angles" are angles whose measures add to 90 degrees. So m<B+ m<C= 90.
"m<B is two more than three times the measure of <C" means that m<B= 3m<C+ 2.
So m<B+ m<C= (3m<C+ 2)+ m<C= 4m<C+ 2= 90. Solve that for m<C then use m<B+ m<C= 90 to find m<B.