Question

In the diagram, what is the measure of angle 1 to the nearest degree?

A transversal intersects 2 lines to form 8 angles. Clockwise from the top left, the angles are blank, 88 degrees, blank, (7 x + 4) degrees; blank, blank, (7 x minus 2) degrees, 1.
82°
92°
94°
98°

Answer 1

At the top intersection the 88° angle and the (7x + 4)° angle are vertical, so they are equal:
88 = 7x + 4 → 7x = 84 → x = 12.

Then (7x − 2)° = 7(12) − 2 = 82°. Angle 1 is adjacent to that 82° angle, so they are supplementary:
angle 1 = 180° − 82° = 98°.

Answer: 98°.