What is the degree measure of the largest angle if the degree measures of the interior angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4?
A. 90 degrees
B. 100 degrees
C. 144 degrees
D. 150 degrees
E. 172 degrees
Answer
The sum of the degree measures of all the angles of ANY quadrilateral is 360 degrees. Let's designate the degree measure of the smallest angle to be X. Therefore, since the degree
measures of the angles are in the ratio 1 : 2 : 3 : 4, and they must sum to 360, we can set up the following equation:
X + 2X + 3X + 4X = 360.
The smallest angle is 36 degrees, so the largest angle is: 4 × 36 = 144 degrees.
Correct Answer: Choice C