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
139°
139 degrees
94°
94 degrees
127°
The sum of the interior angles of a triangle is always 180 degrees. Therefore, the remaining interior angle of the triangle can be found by subtracting the given angles from 180:
180 - 41 - 53 = 86 degrees
Since the exterior angle formed by the extended line is supplementary to the interior angle at the top vertex, angle x is also 86 degrees.
To find the value of angle x, we need to use the fact that the sum of the interior angles of a triangle is always 180 degrees.
Given that the interior angles at the left vertex and the right vertex are 41 degrees and 53 degrees respectively, we can find the value of the interior angle at the top vertex by subtracting the sum of these two angles from 180 degrees.
180 degrees - (41 degrees + 53 degrees) = 180 degrees - 94 degrees = 86 degrees.
Therefore, the value of angle x is 86 degrees.
To find the value of angle x, we need to know the properties of the angles in a triangle. The sum of the interior angles in a triangle is always 180 degrees.
Given that one interior angle is 41 degrees and another is 53 degrees, we can find the value of the third interior angle:
Third interior angle = 180 degrees - (41 degrees + 53 degrees)
Third interior angle = 180 degrees - 94 degrees
Third interior angle = 86 degrees
Now, we need to remember that the exterior angle is equal to the sum of the two opposite interior angles. In this case, angle x is the exterior angle formed when a line extends from the top vertex of the triangle.
Angle x = 41 degrees + 53 degrees
Angle x = 94 degrees
Therefore, the value of angle x is 94 degrees.