Use the image to answer the question.

Question

show me how to solve with the trangle angle sum theorem
An illustration shows a triangle with vertices as A B C. Angle A on top is 120 degrees and angle B on the left is 34 degrees. Vertex C is on the right.

Use the Triangle Angle Sum Theorem to find the measure of the third angle of the triangle shown.

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, you have:

• Angle A = 120 degrees
• Angle B = 34 degrees
• Angle C = ? (this is what we need to find)

To find the measure of angle C, you can use the following formula:

\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]

Substituting the known values:

\[ 120^\circ + 34^\circ + \text{Angle C} = 180^\circ \]

Now, add Angle A and Angle B:

\[ 154^\circ + \text{Angle C} = 180^\circ \]

Next, to find Angle C, subtract the sum of Angle A and Angle B from 180 degrees:

\[ \text{Angle C} = 180^\circ - 154^\circ \]

Calculating that gives:

\[ \text{Angle C} = 26^\circ \]

Thus, the measure of Angle C is 26 degrees.