Question

Use the Triangle Angle Sum Theorem to find the measure of the third angle of the triangle if the measure of two angles are 34.6° and 52.8°.

Answer 1

The Triangle Angle Sum Theorem states that the sum of the measures of the angles in a triangle is always 180°.

Let's denote the measure of the third angle as x.

According to the Triangle Angle Sum Theorem:
34.6° + 52.8° + x = 180°

To find x, we need to isolate it on one side of the equation.
First, combine the known angle measures:
87.4° + x = 180°

Next, isolate x by subtracting 87.4° from both sides:
x = 180° - 87.4°

Simplifying this equation gives:
x = 92.6°

Therefore, the measure of the third angle is 92.6°.