Question
Question
Use the image to answer the question.
An illustration shows a triangle with a 90 degree angle at the top vertex. The interior angle of the left vertex is labeled x. A line extending outward from the right vertex forms an exterior angle of 152 degrees.
Find angle x
.
(1 point)
Responses
62°
62 degrees
118°
118 degrees
28°
28 degrees
90°
Use the image to answer the question.
An illustration shows a triangle with a 90 degree angle at the top vertex. The interior angle of the left vertex is labeled x. A line extending outward from the right vertex forms an exterior angle of 152 degrees.
Find angle x
.
(1 point)
Responses
62°
62 degrees
118°
118 degrees
28°
28 degrees
90°
Answers
Answered by
GPT-4o mini
To find the value of angle \( x \) in the triangle, we can use the property of exterior angles.
The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. In this case, the exterior angle is given as \( 152^\circ \) and corresponds to the interior angles \( x \) and the right angle (which is \( 90^\circ \)).
According to the exterior angle theorem:
\[
\text{Exterior Angle} = \text{Angle 1} + \text{Angle 2}
\]
So we have:
\[
152^\circ = x + 90^\circ
\]
To find \( x \), we subtract \( 90^\circ \) from \( 152^\circ \):
\[
x = 152^\circ - 90^\circ = 62^\circ
\]
Therefore, the measure of angle \( x \) is:
**62°**
The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. In this case, the exterior angle is given as \( 152^\circ \) and corresponds to the interior angles \( x \) and the right angle (which is \( 90^\circ \)).
According to the exterior angle theorem:
\[
\text{Exterior Angle} = \text{Angle 1} + \text{Angle 2}
\]
So we have:
\[
152^\circ = x + 90^\circ
\]
To find \( x \), we subtract \( 90^\circ \) from \( 152^\circ \):
\[
x = 152^\circ - 90^\circ = 62^\circ
\]
Therefore, the measure of angle \( x \) is:
**62°**