Question

An angle measures 26° less than the measure of its supplementary angle. What is the measure of each angle?

Answer 1

Given:

• Supplementary angle₁ = Supplementary angle₂ - 26

We already know that the sum of two supplementary angles must be equivalent to 180°. Therefore, we obtain the following equation:

• ⇒ Supplementary angle₁ + Supplementary angle₂ = 180°

When we plug the value of "the first supplementary angle", we get:

• ⇒ Supplementary angle₂ - 26 + Supplementary angle₂ = 180°

When simplified, we get:

• ⇒ 2(Supplementary angle₂) - 26 = 180°

• ⇒ 2(Supplementary angle₂) = 180 + 26

• ⇒ 2(Supplementary angle₂) = 206

• ⇒ Supplementary angle₂ = 103°

Therefore, the measure of the second supplementary angle is 103°. Now, let's substitute the measure of the second supplementary angle into the given equation to determine the measure of the first supplementary angle.

• ⇒ Supplementary angle₁ = Supplementary angle₂ - 26

• ⇒ Supplementary angle₁ = 103 - 26

• ⇒ Supplementary angle₁ = 77°

Therefore, the measure of the first supplementary angle is 77°.