Use the image to answer the question.

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°
90 degrees
Remaining Attempts : 3

Answer 1

To find angle \( x \) in the triangle with a right angle at the top vertex, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

We know:

1. The right angle at the top vertex is 90 degrees.
2. The exterior angle at the right vertex is 152 degrees.

An exterior angle is equal to the sum of the two remote interior angles of the triangle. Therefore, we can express this relationship as follows:

\[ \text{Exterior angle} = \text{Angle at left vertex (x)} + \text{Right angle (90 degrees)} \]

Plugging in the values we have:

\[ 152 = x + 90 \]

To isolate \( x \), subtract 90 degrees from both sides:

\[ 152 - 90 = x \] \[ 62 = x \]

Therefore, angle \( x \) is \( 62 \) degrees.

The correct response is: 62°