Use the image to answer the question.

Question

An illustration shows a triangle with vertices as B C D. Angle C on the top is labeled as a question mark and angle D on the bottom right is labeled as 22 degrees. Vertex B is on the bottom left. The horizontal line D B extends beyond the triangle to the left with an arrow at the end, and a point A is marked on it. The angle of A B C is labeled as 103 degrees.

Use the Triangle Angle Sum Theorem to find the measure of the angle on point C
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(1 point)
°

Answer 1

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

Let:

• Angle C = x (the angle we want to find)
• Angle D = 22 degrees
• Angle A = 103 degrees

However, we also have to consider angle A as it lies outside of triangle BCD. The angle ABC is an exterior angle to triangle BCD and is equal to the sum of the opposite interior angles (angle D + angle C).

Using this information, we have the following equation based on the exterior angle theorem:

\[ \text{Angle A} = \text{Angle D} + \text{Angle C} \]

Substituting the known values:

\[ 103 = 22 + x \]

Now, solve for x (angle C):

\[ x = 103 - 22 \] \[ x = 81 \]

Therefore, angle C measures 81 degrees.