What is the measure of the exterior angle x?

Question

An illustration shows a triangle with an interior angle at the top vertex of 37 degrees and an interior angle at the right vertex of 42 degrees. A line extending outward from the left vertex forms an exterior angle that is labeled x.

(1 point)
Responses

37°
37 degrees

79°
79 degrees

42°
42 degrees

59°

Answer 1

To find the measure of the exterior angle \( x \) at the left vertex of the triangle, we can first find the measure of the third interior angle of the triangle. The sum of the interior angles of a triangle is always \( 180^\circ \).

Given:

• The top vertex angle is \( 37^\circ \).
• The right vertex angle is \( 42^\circ \).

We can find the third angle as follows:

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

Now, the exterior angle \( x \) at the left vertex is equal to the sum of the measures of the two remote interior angles (the angles at the top and right vertex). Therefore:

\[ x = 37^\circ + 42^\circ = 79^\circ. \]

Thus, the measure of the exterior angle \( x \) is \( 79^\circ \).

The answer is:

79°