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.

Question

Find angle x
.

(1 point)
Responses

90°
90 degrees

62°
62 degrees

118°
118 degrees

28°

Answer 1

In a triangle, the sum of the interior angles is always 180 degrees. Given that one angle is 90 degrees and the angle at the left vertex is labeled \( x \), we can express the angle at the right vertex.

Since the exterior angle at the right vertex is \( 152^\circ \), we can use the exterior angle theorem which states that an exterior angle is equal to the sum of the two opposite interior angles. Thus, we have:

\[ \text{Exterior angle} = \text{Interior angle at left} + \text{Interior angle at right} \]

Let the interior angle at the right vertex be \( 90^\circ - x \). Then according to the exterior angle theorem:

\[ 152^\circ = x + (90^\circ - x) \]

Simplifying this gives:

\[ 152^\circ = 90^\circ \]

Since this isn't true, let's reconsider what the information provided indicates. We deduce that:

\[ 152^\circ = 90^\circ + x \]

Solving for \( x \):

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

Thus, angle \( x \) is \( 62^\circ \).

The correct answer is:

62°