Two Adjacent Angles of a Parallelogram are in the Ratio of 1:3 GMAT Problem Solving

Question: Two adjacent angles of a parallelogram are in the ratio of 1:3. What is the smaller angle of the two?

1. 30.
2. 45.
3. 90.
4. 135.
5. 180.

“Two adjacent angles of a parallelogram are in the ratio of 1:3.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2021”. 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.

Solution and Explanation:

Approach Solution 1:

It is given in the question that there is a parallelogram having two adjacent angles in the ratio of 1:3. It has asked to find out the smaller of the two angles.
This is a question from geometry.
There is a property of a parallelogram that the sum of two adjacent angles in a parallelogram is 180 degrees.
For example, if one angle is 80 degrees then the other angle has to be 180 - 80 = 100 degrees so that the sum of angles will be 180 degrees.
Coming back to the question.
We have
a parallelogram having two adjacent angles in the ratio of 1:3.
Let the smaller angle be x
So the larger angle will be 3x
Now we know that the sum of two adjacent angles in a parallelogram is 180 degrees.
We have,
X + 3x = 180
4x = 180
X = 180/4
X = 45
The smaller angle is 45 degrees.

Correct Answer: B

Approach Solution 2:

It is given in the question that there is a parallelogram having two adjacent angles in the ratio of 1:3. It has asked to find out the smaller of the two angles.
There is a property of a parallelogram that the sum of two adjacent angles in a parallelogram is 180 degrees.
Therefore the two angles will be 1/(1+3) * 180 degrees and 3/(1+3) * 180 degrees.
We are asked to find out the smaller angle.
Therefore smaller angle will be
1/(1+3) * 180 = 180/4 = 45

Correct Answer: B

Approach Solution 3

Given, two adjacent angles of a parallelogram are in the ratio 1 : 3

We have to find the measure of the angles.

A parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal.

Let the angles be x and 3x.

From the properties of a parallelogram, the sum of adjacent angles are supplementary.

So, x + 3x = 180°

4x = 180°

x = 180°/4

x = 45°

Therefore, the required measures of the angle are 45°

Correct Answer: B

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