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.

Question

Find angle x
.

(1 point)
Responses

127°
127 degrees

86°
86 degrees

139°
139 degrees

94°

Answer 1

To find the measure of the exterior angle $x$ formed by extending a line from the top vertex of the triangle, we can use the properties of triangles and exterior angles.

1. First, we note that the sum of the interior angles of a triangle is always 180 degrees. In this case, we have two of the interior angles:

   • Left angle: 41 degrees
   • Right angle: 53 degrees

2. We can calculate the third interior angle $A$: $$A={180}^{\circ }-({41}^{\circ }+{53}^{\circ })$$ $$A={180}^{\circ }-{94}^{\circ }={86}^{\circ }$$

3. The exterior angle $x$ at the top vertex of the triangle is equal to the sum of the two remote (non-adjacent) interior angles, which are the angles at the left and right vertices: $$x={41}^{\circ }+{53}^{\circ }$$ $$x={94}^{\circ }$$

Thus, the value of angle $x$ is ${94}^{\circ }$.

So the correct response is: 94°