Question

Two angles in a triangle measure 102 degrees and 67 degrees. What is the measure of the third angle?

Answer 1

To find the measure of the third angle in a triangle, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

Let the measures of the two given angles be:
- Angle A = 102 degrees
- Angle B = 67 degrees

We need to find Angle C. We can use the formula:

\[
Angle C = 180 - (Angle A + Angle B)
\]

Substituting the values we have:

\[
Angle C = 180 - (102 + 67)
\]

Calculating the sum of Angle A and Angle B:

\[
Angle A + Angle B = 102 + 67 = 169
\]

Now, we subtract this sum from 180:

\[
Angle C = 180 - 169 = 11
\]

Thus, the measure of the third angle is \( \boxed{11} \) degrees.