Question

Jack uses triangles in the construction of bridges, such as the one shown below. a triangle has angles g, 72 degrees, and blank. the exterior angle to the blank angle is 133 degrees. what is the measure of angle?

A. 47°
B. 61°
C. 108°
D. 119°

Answer 1

The measure of the unknown angle in the triangle is 61 degrees, found by using the fact that interior and exterior angles are supplementary and the sum of angles in a triangle is 180 degrees.The correct answer is B.

Step-by-step explanation:

To find the measure of the unknown angle in the triangle, we use the fact that the sum of angles in a triangle is 180 degrees. Given that one angle is 72 degrees and the exterior angle to the unknown angle is 133 degrees, we can find the measure of this exterior angle by remembering that interior and exterior angles are supplementary, meaning they add up to 180 degrees. Therefore, the interior angle can be found using the equation:

Interior Angle + Exterior Angle = 180°

Interior Angle = 180° - 133°

Interior Angle = 47°

Now that we have the two angles (72° and 47°), we can find the third angle by subtracting their sum from 180°:

Third Angle = 180° - (72° + 47°)

Third Angle = 180° - 119°

Third Angle = 61°

Therefore, the measure of the unknown angle is 61 degrees, which corresponds to option B.