Use the image to answer the question.

Question

A 103
C ?
D 22

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

(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
m∠
c = Response area°

Answer 1

To find the measure of angle \( C \) using the Triangle Angle Sum Theorem, we can use the fact that the sum of the angles in a triangle is always \( 180^\circ \).

Given:

• \( m\angle A = 103^\circ \)
• \( m\angle D = 22^\circ \)

We can denote the measure of angle \( C \) as \( m\angle C \). According to the Triangle Angle Sum Theorem:

\[ m\angle A + m\angle C + m\angle D = 180^\circ \]

Substituting the known values:

\[ 103^\circ + m\angle C + 22^\circ = 180^\circ \]

Now combine the known angles:

\[ 125^\circ + m\angle C = 180^\circ \]

To isolate \( m\angle C \), subtract \( 125^\circ \) from both sides:

\[ m\angle C = 180^\circ - 125^\circ \]

\[ m\angle C = 55^\circ \]

So the measure of the angle at point \( C \) is \( 55^\circ \).

Final Answer:

m∠
c = 55°