Question
What is the measure of the exterior angle x ? (1 point)
37 on one angle and 42
37 on one angle and 42
Answers
Answered by
GPT-4o mini
To find the measure of the exterior angle \( x \) in a triangle, you can use the property that the exterior angle is equal to the sum of the two remote interior angles.
In this case, you have two angles of the triangle given as \( 37^\circ \) and \( 42^\circ \). Let's call the third angle \( y \).
The sum of the interior angles of a triangle is always \( 180^\circ \):
\[
37^\circ + 42^\circ + y = 180^\circ
\]
Calculating \( y \):
\[
y = 180^\circ - 37^\circ - 42^\circ = 180^\circ - 79^\circ = 101^\circ
\]
Now, if \( x \) is the exterior angle corresponding to the angle \( y \), then:
\[
x = 37^\circ + 42^\circ
\]
Calculating \( x \):
\[
x = 37^\circ + 42^\circ = 79^\circ
\]
Therefore, the measure of the exterior angle \( x \) is \( \mathbf{79^\circ} \).
In this case, you have two angles of the triangle given as \( 37^\circ \) and \( 42^\circ \). Let's call the third angle \( y \).
The sum of the interior angles of a triangle is always \( 180^\circ \):
\[
37^\circ + 42^\circ + y = 180^\circ
\]
Calculating \( y \):
\[
y = 180^\circ - 37^\circ - 42^\circ = 180^\circ - 79^\circ = 101^\circ
\]
Now, if \( x \) is the exterior angle corresponding to the angle \( y \), then:
\[
x = 37^\circ + 42^\circ
\]
Calculating \( x \):
\[
x = 37^\circ + 42^\circ = 79^\circ
\]
Therefore, the measure of the exterior angle \( x \) is \( \mathbf{79^\circ} \).