Answer:
x = 124
Explanation:
You want the value of the exterior angle x°, given that the remote interior angles are 83° and 41°.
Exterior angle
The exterior angle of a triangle is equal to the sum of the remote interior angles:
x° = 83° +41°
x° = 124°
x = 124
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Check
The interior angle adjacent to x° is its supplement:
180° -124° = 56°
The sum of the interior angles of the triangle is 180°:
83° +41° +56° = 180° . . . . . true
The theorem we cite above is a consequence of the fact that the missing interior angle is supplementary to both x° and the sum of the other two interior angles. It saves having to find the measure of the missing interior angle.