The measure of an angle is 10 less than half its supplement. What is the measure of the angle?

Answer 1

The measure of an angle is 10 less than half its supplement. What is the measure of the angle?

Angle A and it's Supplement is B

A + B = 180

A = 1/2 B - 10

1/2 B - 10 + B = 180

3/2 B = 190

B = 190 * (2/3)

B = 380 / 3

B = 126.67

A = 53.33

Answer 2

In this problem, we must start by remembering that an angle is considered a supplement only if it, and the other angle, add up to 180 degrees. So here, we know that:

Angle 1 (a₁) and Angle 2 (a₂) must add up to 180

Angle 1 (a₁) is "10 less than half" of Angle 2 (a₂) -> Here we have defined a₂ as the supplement and a₁ as the angle being asked for.

In equation form, we would consider these as:

a₁ + a₂ = 180, given that a₁ = a₂/2 -10.

We place the second equation into the first one, and we get:

a₂/2-10 + a₂ = 180

1.5a₂ =190

a₂ = 126.666° (you could round to 127°, if you wanted)

a₁ = 53.333° (you could round to 53°, if you wanted) -> this is the answer