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 using the Triangle Angle Sum Theorem, we can use the following steps:

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

2. In triangle BCD, we know the measures of angles D and A B C:

   • Angle D = 22 degrees
   • Angle A B C = 103 degrees

3. We can represent angle C with the variable \( x \). According to the Triangle Angle Sum Theorem: \[ \text{Angle B} + \text{Angle C} + \text{Angle D} = 180 \text{ degrees} \] Substituting the known values gives us: \[ 103 + x + 22 = 180 \]

4. Now, simplify the equation: \[ 125 + x = 180 \]

5. To find \( x \), subtract 125 from both sides: \[ x = 180 - 125 \] \[ x = 55 \]

Thus, the measure of angle C is 55 degrees.