Problem:
The angles of quadrilateral ABCD satisfy ∠A=2∠B=3∠C=4∠D. What is the degree measure of ∠A, rounded to the nearest whole number?
Answer Choices:
A. 125
B. 144
C. 153
D. 173
E. 180
Solution:
Let x be the degree measure of ∠A. Then the degree measures of angles B,C, and D are x/2,x/3, and x/4, respectively. The degree measures of the four angles have a sum of 360, so
360=x+2x​+3x​+4x​=1225x​
Thus x=(12⋅360)/25=172.8≈(D)173​.
The problems on this page are the property of the MAA's American Mathematics Competitions