Two angles are complementary (the sum of the two angles is 90 degrees). The sum of the first angle plus twice the second angle is 150 degrees. Find the measures of the angles.

Answer 1

Let the first angle be x and the 2nd angle be y, then x + y = 90° , and x + 2y = 150° now solve two equations two unknowns

x + y = 90° (1)

x + 2y = 150° (2) Subtract (2) from (1) , Multiply (2) by -1, and add (1) and (2)

x + y = 90° °(1)

-x - 2y = -150° (2) , -y = -60° , y =60°°, and x = 90° - y = 90° -60° = 30° Check

x + y = 90° , 30° + 60° = 90°

x + 2y = 150°, 30° + 2( 60°) = 30° + 120° = 150° Checks

Answer 2

a represents the measure of the first angle

90 - a represents the measure of the second angle

a + 2(90 - a) = 150

Can you solve for a and answer?