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°

1 answer

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°