Complementary & Supplementary Angles

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In summary, for the first question, the measure of <P is 2m<Q- 3 and the measure of <Q is m<Q. For the second question, the measure of <B is 3m<C+ 2 and the measure of <C is m<C.
  • #1
bernardl
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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.
 
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Hello! :D

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  • #3
I honestly don't know how to do both of those questions!
 
  • #4
O.k., let's try the first one. mP + mQ = 180 degrees. mP = 2mQ - 3. Make sense? Can you solve it now?
 
  • #5
"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.
 

FAQ: Complementary & Supplementary Angles

What are complementary angles?

Complementary angles are two angles that add up to 90 degrees. In other words, when placed adjacent to each other, they form a right angle.

How do you find complementary angles?

To find complementary angles, subtract the given angle from 90 degrees. The resulting angle will be its complementary angle. For example, if an angle measures 30 degrees, its complementary angle would be 90 - 30 = 60 degrees.

What are supplementary angles?

Supplementary angles are two angles that add up to 180 degrees. When placed adjacent to each other, they form a straight line.

How do you find supplementary angles?

To find supplementary angles, subtract the given angle from 180 degrees. The resulting angle will be its supplementary angle. For example, if an angle measures 120 degrees, its supplementary angle would be 180 - 120 = 60 degrees.

Can complementary angles also be supplementary angles?

No, complementary angles and supplementary angles are mutually exclusive. If two angles are complementary, they cannot be supplementary and vice versa. However, two angles can be both complementary and supplementary if they both measure 90 degrees.

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