Question

Use the image to answer the question.



An illustration shows a triangle with an interior angle at the left vertex of 41 degrees and an interior angle at the right vertex of 53 degrees. A line extending from the top vertex forms an exterior angle that is labeled x.
Find angle x.

(1 point)
Responses

86°
86 degrees

94°
94 degrees

139°
139 degrees

127°

1 answer

To find the value of angle \( x \), which is the exterior angle at the top vertex of the triangle, we can use the properties of angles in a triangle.

First, we calculate the third interior angle of the triangle. The sum of the interior angles of a triangle is always \( 180^\circ \). Given the interior angles are \( 41^\circ \) and \( 53^\circ \), we find the third angle as follows:

\[ \text{Third angle} = 180^\circ - 41^\circ - 53^\circ \]

Calculating this gives:

\[ \text{Third angle} = 180^\circ - 94^\circ = 86^\circ \]

Now, the exterior angle \( x \) at the top vertex is equal to the sum of the two opposite interior angles (the angles that are not adjacent to \( x \)). Therefore, we have:

\[ x = 41^\circ + 53^\circ \]

Calculating this gives:

\[ x = 94^\circ \]

Thus, the value of angle \( x \) is:

\[ \boxed{94^\circ} \]