Geometry math equation

Question

Angle one is supplementary to angle to an angle two is complementary to angle three. If the measure of angle one equals 165°, then what are the measures of the other two angles?

Answer 1

Algebra wise (using < to mean angle):

<1 + <2 = 180 [supplementary]

=> <2 = 180 - <1

and

<2 + < 3 = 90 [complementary]

=> <3 = 90 - <2

and

<1 + <2 + <3 = x

hence, given any one angle, you can find the other two and the sum of all three.

Answer 2

Hello Brit,

I recently saw your question re: angle measurements and wanted to provide some guidance.

If I'm reading the question correctly, you have Angle 1, Angle 2 and Angle 3.

The key here is remembering the definitions/descriptions of what make angles complementary to each other or supplementary to each other. Two angles that are complementary to each other have measurements which when added together add up to 90 degrees. Two angles that are supplementary to each other have measurements which when added together add up to 180 degrees.

If the measure of Angle 1 is 165 degrees and the question states that it is supplementary to Angle 2, you need to find the degree measurement which when added to Angle 1 adds to 180 degrees. That gives you the measure of Angle 2. Because the question states that Angle 2 is complementary to Angle 3, then the measure of Angle 2 plus the measure of Angle 3 add up to 90 degrees. Since you solved for the measure of Angle 2 earlier, you need to find the degree measurement which when added to Angle 2 adds to 90 degrees.

Let me know if that wasn't clear and I'll try to help further. Thanks.