Find the value of x given that the angles are equal.

Published on February 2, 2025

Geometry

The sum of three angles around a point, 2x, x, and x, equals 360 degrees, leading to the solution x = 90 degrees.

Question

Answer

The problem involves finding the value of

from the given angles around a point.
From the image, we can see that there are three angles around a point, which are

, and

The sum of angles around a point is always

.
Therefore, we can write the equation as:

Combine the terms with

To solve for

, divide both sides of the equation by 4:

Calculate the value of

To verify the answer, substitute

back into the angles:
Angle 1:

Angle 2:

Angle 3:

Sum of the angles:

The sum of the angles is indeed

, which confirms our solution is correct.

Final Answer: The final answer is

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