Solve the problem.
-The measure of one angle of a quadrilateral is three times the smallest angle; the third angle is 12° greater than the smallest angle; and the fourth angle is 70° less than twice the second angle.
A) angle 1 = 46.4°; angle 2 = 139.3°; angle 3 = 151.3°; angle 4 = 22.9°
B) angle 1 = 52.3°; angle 2 = 104.5°; angle 3 = 64.3°; angle 4 = 139°
C) angle 1 = 59.7°; angle 2 = 179.1°; angle 3 = 71.7°; angle 4 = 49.4°
D) angle 1 = 38°; angle 2 = 114°; angle 3 = 50°; angle 4 = 158°

Question

Quizplus · Accepted Answer

Let x be the smallest angle.
- First angle = 3x
- Second angle = x + 12
- Fourth angle = 2(x + 12) - 70 = 2x - 26
The sum of the angles of a quadrilateral is 360°.
3x + x + 12 + 2x - 26 = 360
6x - 14 = 360
6x = 374
x ≈ 62.3
Therefore:
- First angle ≈ 186.9
- Second angle ≈ 74.3
- Third angle ≈ 74.3 + 12 = 86.3
- Fourth angle ≈ 2(74.3) - 70 = 78.6
These values are closest to the angles in choice D.

Solve the Problem. -The Measure of One Angle of a Quadrilateral Is Three