Question

two of the angles in a triangle are complementary. the third angle is twice the measure of one of the complementary angles. what is the measure of each of the angles? ​

Answer 1

The triangle has three angles, A, B, and C, with

A+B=π2,(1)

and

C=2A.(2)

As with all triangles,

A+B+C=π.(3)

Inserting equations (1) and (2) into equation (3) gives

π2+2A=π,(*)

so

A=π4.(4)

Combining equations (1) and (4) gives

B=π4.(5)

Combining equations (3)-(5) gives

C=π.(6)

(All angular units here are radians.)