Question

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

The image shows a triangle. There are three letters: b, a, and c. Next to b there is the number: 34 degrees. Next to a there is the number: 120 degrees

Answer 1

Correct good job

Answer 2

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

Given the measures of two angles in the triangle:
- Angle a = 120 degrees
- Angle b = 34 degrees

To find the measure of the third angle (let's call it angle c), we can use the following equation:

\[
\text{Angle a} + \text{Angle b} + \text{Angle c} = 180^\circ
\]

Substituting the known values:

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

Now, add the measures of angle a and angle b:

\[
120^\circ + 34^\circ = 154^\circ
\]

Now, we have:

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

To find angle c, subtract 154 degrees from both sides:

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

Therefore, the measure of the third angle (angle c) is **26 degrees**.