Question

what is the value of x? 127° 49° a. 102 b. 106 c. 98 d. 176

Explanation:

Step1: Find the non - 127° adjacent angle

The angle adjacent to 127° on a straight - line sums to 180° with 127°. Let this angle be y. So, $y = 180^{\circ}-127^{\circ}=53^{\circ}$.

Step2: Use the angle - sum property of a triangle

In a triangle, the sum of the interior angles is 180°. We know two angles of the triangle: y = 53° and 49°. Let the third angle be z. Then $z=180^{\circ}-(53^{\circ} + 49^{\circ})=180^{\circ}-102^{\circ}=78^{\circ}$.

Step3: Find the value of x

The angle x and z are supplementary (form a straight - line). So, $x = 180^{\circ}-78^{\circ}=102^{\circ}$.

Answer:

A. 102