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

90°
90 degrees

118°
118 degrees

28°
28 degrees

62°

Answer 1

To find angle \( x \), we can use the property of exterior angles in a triangle. The exterior angle is equal to the sum of the two opposite interior angles.

In this case, the exterior angle is 152 degrees. Since the triangle has a right angle of 90 degrees at the top vertex, we can express the relationship as follows:

\[ \text{Exterior angle} = \text{Interior angle (top vertex)} + \text{Interior angle (left vertex)} \]

Let the left vertex angle be \( x \). Therefore, we have:

\[ 152° = 90° + x \]

Now, we can solve for \( x \):

\[ x = 152° - 90° \] \[ x = 62° \]

Thus, angle \( x \) is \( 62° \).

The correct answer is:

62°