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

90°
90 degrees

28°

Answer 1

To find angle \( x \) in the triangle, we can use the properties of angles in a triangle and the exterior angle.

The exterior angle (which is 152 degrees) is equal to the sum of the two remote interior angles in the triangle. In this case, the two remote interior angles are angle \( x \) and the right angle, which is 90 degrees.

So we can write the equation:

\[ 152 = x + 90 \]

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

1. Subtract 90 from both sides:

   \[ x = 152 - 90 \]

2. Perform the subtraction:

   \[ x = 62 \]

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

The correct answer is:

62°.