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°
11 answers