Question

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

Answer 1

Answer:

The measure of the third angle is a 90 degrees

Step-by-step 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