Question

There is a triangle. Three angles. One angle is 37 degrees, one angle is 42 degrees, what is the measure of the exterior angle that isn't shown.

Answer 1

In a triangle, the sum of the interior angles is always 180 degrees. Given two angles of the triangle: 37 degrees and 42 degrees, we can find the measure of the third interior angle.

First, we can calculate the third angle:

\[
\text{Third angle} = 180^\circ - (37^\circ + 42^\circ) = 180^\circ - 79^\circ = 101^\circ
\]

Now, to find the exterior angle corresponding to the third angle, we can use the fact that an exterior angle is equal to the sum of the two non-adjacent interior angles. Alternatively, the exterior angle can also be calculated as follows:

\[
\text{Exterior angle} = 180^\circ - \text{Interior angle}
\]
For the third angle, this will be:

\[
\text{Exterior angle} = 180^\circ - 101^\circ = 79^\circ
\]

Thus, the measure of the exterior angle that corresponds to the third angle is **79 degrees**.