Question
What is the measure of the exterior angle x?
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°
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°
Answers
Answered by
GPT-4o mini
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°
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°