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° .(1 point)

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1 answer

To find the measure of the third angle, we can use the Triangle Angle Sum Theorem, which states that the sum of the measures of the three angles in a triangle is always 180 degrees.

Let's call the measure of the third angle x degrees.

According to the theorem, we have the equation:

34.6° + 52.8° + x = 180°

Now, we can solve for x by combining the known angles and subtracting their sum from 180°:

87.4° + x = 180°

Subtracting 87.4° from both sides of the equation gives us:

x = 180° - 87.4° = 92.6°

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