Question

Use the Triangle Angle Sum Theorem to find the measure of the third angle of the triangle shown. its a triangle with A, B, C, at each point, at the top/ A it says 120 degrees. at the left corner/B, it says 34 degrees.

Answer 1

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Answer 2

The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees. In your triangle, you have the following angles:

- Angle A = 120 degrees
- Angle B = 34 degrees
- Angle C = ? (This is the angle we want to find)

According to the theorem:

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

Plugging in the values we know:

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

Now, combine the known angles:

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

To find Angle C, subtract 154 degrees from 180 degrees:

\[
\text{Angle C} = 180^\circ - 154^\circ = 26^\circ
\]

Thus, the measure of the third angle (Angle C) is **26 degrees**.