What do we know about the angle measures of a triangle?
58^(∘)
Practice makes perfect
Consider the following diagram of a triangular window.
We want to find the measure of the numbered angle. To do so, we will start by labeling the vertices of the triangle.
We are given the measure of the angles at A and C and are asked to find the measure of the angle at B. Since we have two of the three interior angles, we can recall the Triangle Angle Sum Theorem.
Triangle Angle Sum Theorem
The sum of the angle measures in a triangle is 180^(∘).
We can use this to set up and solve an equation for m∠B.
m∠ A+m∠ B+m∠ C=180^(∘)
Since the measures of two angles are given, this lets us find the measure of the third angle. We will substitute m∠ A= 59^(∘) and m∠ C= 63^(∘) into the above equation and solve it for m∠ B. Let's do it!
