Question: The exterior angles of a quadrilateral are in the ratio 1 : 4 : 4 : 6. What is the difference between the largest and the smallest interior angles of the quadrilateral?

1. 140
2. 120
3. 110
4. 100
5. 60

Answer:

Approach Solution (1):

The sum of the exterior angles of a quadrilateral is 360
x + 4x + 4x + 6x = 360
15x = 360

x = \(\frac{360}{15}=24\)

Interior and Exterior angles of a quadrilateral are corresponding to each other.
So smallest interior angle = x = 24
Largest interior angle = 6x = 6 * 24 = 144

Difference between the smallest and the largest interior angle = 144 – 24 = 120

Correct Option: B

Approach Solution (2):

Sum of the exterior angles is 360
Largest exterior angle = \(\frac{6}{15}*360=144\)
Smallest exterior angle = \(\frac{1}{15}*360=144\)
Largest interior angle = 180 – 24 = 156
Smallest interior angle = 180 – 144 = 36
Their difference = 156 – 36 = 120

Correct Option: B

“The exterior angles of a quadrilateral are in the ratio 1 : 4 : 4 : 6. What is the difference between the largest and the smallest interior angles of the quadrilateral?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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