Exterior and interior angles of a triangle are complementary.
D
Practice makes perfect
Let's find the value of the interior angles of an equiangular triangle, and then calculate the value of the exteriors angles.
Interior Angles
To find the measure of the interior angles, we first must consider the fact that the sum of the angles of every triangle is 180^(∘).
m∠ 1+m∠ 2+m∠ 3=180^(∘)
An equiangular triangle is a triangle with angles that all have the same measure. Because they are the same, we can substitute m∠ 2 and m∠ 3 with m∠ 1. We get the following equation.
m∠ 1+ m∠ 1+ m∠ 1=180^(∘)
Let's solve and find the value of each angle in an equiangular triangle.
The measure of each angle in an equiangular triangle is 60^(∘).
Exterior Angles
Now, let's draw an equiangular triangle and find its exterior and interior angles.
Let's call one of the exterior angles ∠ 2. Notice that ∠ 1 and ∠ 2 are complementary angles. This means that the sum of their measures is 180^(∘).
m∠1+m∠ 2=180^(∘)
From the previous part, we know that m∠ 1 equals 60^(∘). Let's substitute this value into the equation and then solve for m∠ 2.
Note, since the measures of all interior angles are equal, the measures of all exterior angles are also the same. Therefore, the measure of each exterior angle of an equiangular triangle is 120^(∘). The answer is D.
