Use the Triangle Angle Sum Theorem to find the measure of the angle on point C.

Question

The image shows a triangle. C is the angle at the top. D is the angle at the bottom right corner. Inside the angle of D, is the number 22 degrees. The bottom line of the triangle, which is attached to the triangle, is an arrow pointing left. Next to the arrow is a colored in dot. Underneath the dot is the letter A. At the bottom left angle of the triangle is the letter B. Above B is the number 103 degrees.

Answer 1

The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.

In your triangle, we have:

• Angle A = 103 degrees
• Angle D = 22 degrees (this is the angle at point D, which is adjacent to angle C)
• We need to find the measure of angle C.

To find angle C, we first need to calculate the sum of angles A and D:

\[ A + D = 103^\circ + 22^\circ = 125^\circ \]

Now, since the sum of all angles in a triangle is 180 degrees, we can find angle C by subtracting the sum of angles A and D from 180 degrees:

\[ C = 180^\circ - (A + D) = 180^\circ - 125^\circ = 55^\circ \]

Thus, the measure of angle C is 55 degrees.