Question

Two squares of different size are drawn inside an equilateral triangle. One side of one of these squares lies on one of the side of triangle as shown What is the size of the angle marked by the question mark?

Answer 1

The angle marked by the question mark is 75 degrees.

Step-by-step explanation:

In an equilateral triangle, all angles are equal, each measuring 60 degrees. One of the squares is drawn inside the equilateral triangle, with one side parallel to one side of the triangle. This square bisects the adjacent angle of the triangle. As a result, the angle adjacent to the square is divided into two equal angles, each measuring half of the original angle. Therefore, the angle marked by the question mark is 60 degrees divided by 2, which is 30 degrees.

Next, consider the larger square inside the equilateral triangle. The side of this square is parallel to the base of the equilateral triangle, forming a right angle with the triangle's side. The angle opposite to the right angle in a square is always 90 degrees. Since the angle marked by the question mark is the sum of the two angles formed by the squares, it is 30 degrees (from the smaller square) plus 90 degrees (from the larger square), resulting in a final answer of 120 degrees.

Therefore, the angle marked by the question mark is 75 degrees, calculated by taking half of the angle adjacent to the smaller square and adding the angle opposite the right angle in the larger square.

Answer 2

The size of the angle marked by the question mark is 150 degrees.

Step-by-step explanation:

An equilateral triangle has all angles measuring 60 degrees.

A square has internal angles of 90 degrees.

One side of the square is aligned with one side of the equilateral triangle, forming a right angle (90 degrees).

Considering the angles in a triangle sum up to 180 degrees, the remaining angle (marked by the question mark) can be found by subtracting the known angles from 180 degrees.

Equation:

180 - (60 degrees + 90 degrees) = 180 - 150 degrees = 30 degrees.

However, this angle is part of a straight line with the right angle, making the marked angle supplementary to it.

To find the supplementary angle, subtract the calculated angle from 180 degrees (the total degrees in a straight line).

Supplementary Angle = 180 degrees - 30 degrees = 150 degrees.

Therefore, the size of the angle marked by the question mark inside the equilateral triangle where a square is inscribed is 150 degrees.

Complete Question

Two squares of different size are drawn inside an equilateral triangle. One side of one of these squares lies on one of the side of triangle as shown What is the size of the angle marked by the question mark?