An Equilateral Triangle is Constructed on Each Side of a Square GMAT Problem Solving

Question: An equilateral triangle is constructed on each side of a square. What is the sum of the measures of the angles marked?

1. 400°
2. 450°
3. 600°
4. 750°
5. 900°

“An equilateral triangle is constructed on each side of a square.”- 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 An equilateral triangle is constructed on each side of a square. What is the sum of the measures of the angles marked?

Each angle in an equilateral triangle equals 60 because we know that all of its sides are equal.
A square's angles are all 90°.
The diagram shows 4 identified angles. Let's assess one
The highlighted area's overall angle is 360°.
Each highlighted angle has two equilateral triangle angles plus one square angle.
360∘ = 60∘ + 60∘ + 90∘ + x
X∘ = 360 - 210 = 150

A marked angle has a value of 150
Total of the four specified angles is 600.

Correct Answer: C

Approach Solution 2:

There is another approach to answering this question

it is given An equilateral triangle is constructed on each side of a square. What is the sum of the measures of the angles marked?

A point's sum of angles is 360 degrees.

An equilateral triangle has 60 degrees as each angle.
Inside the square, each angle is 90 degrees.

As a result, according to the diagram, one marked angle is = = 360 – 2(times Equilateral triangle)- one angle of the square
= 150

As a result, the total marked angle is equal to the number of marked angles times the value of each marked angle,
= 4X150 = 600

Correct Answer: C

Approach Solution 3:

We know that all sides of an equilateral triangle are equal, so each angle equals 60∘60∘
Each angle of a square is 90°.

There are 4 marked angles in the diagram. Lets evaluate one

Total angle of the marked area = 360 degrees.

Each marked angle has 2 angles of an equilateral triangle + one angle of a square
360= 60 + 60 + 90 + x

X = 360-210 = 150

Angle of one marked angle is 150

Sum of 4 marked angles is 600

Correct Answer: C

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