Question

if two angles of a triangle are complementary find the number of degrees in the third angle of the triangle

Answer 1

The measure of the third angle is a 90 degrees

Explanation:

Let

A and B ----> two complementary angles in a triangle

C ---> the measure of the third angle in a triangle

we know that

If two angles are complementary, then their sum is equal to 90 degrees

so

`A+B=90^o` ---> equation A

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

`A+B+C=180^o` ----> equation B

substitute equation A in equation B

`(90^o)+C=180^o`

solve for C

subtract 90 degrees both sides

`C=180^o-90^o`

`C=90^o`

therefore

we have a right triangle