Solving For Measures of Angles

Question

Two angles form a linear pair. One angle is 1/3 of the other angle.

Answer 1

Answer 2

A linear pair of angles is formed when two lines intersect. The linear pairs are adjacent angles whose sum is 180°.

We are told that the two angles we are solving for are a linear pair, so their sum must be 180°. Let's call angle 1 "A" and angle 2 "B".

A + B = 180° equation (1)

We are also told that one angle is 1/3 the measure of the other angle. Let's assume B is the bigger angle, so:

A = 1/3 * B equation (2)

Now, we have two equations and two variables, so we can solve the system of equations. Equation (2) is already solved for A, so let's substitute 1/3 * B into equation (1) in place of A.

(1/3 * B) + B = 180°

4/3 * B = 180°

B = 180° * 3/4 = 135°

Now that we know B, we can solve for A using equation (1).

A + 135° = 180°

A = 180° - 135° = 45°

As a final check (optional), we can make sure that angle A is 1/3 of angle B as specified.

1/3 * B = 1/3 * 135° = 45° = A