Find the value of x in a triangle problem.

Published on November 3, 2024

Geometry

To find x, the exterior angle theorem is used, along with the knowledge that a right angle is 90 degrees, to solve for x, which equals 45 degrees.

Question

Answer

Here’s how to solve for

Exterior Angle Theorem: The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. In this case, the exterior angle is equal to the sum of the two interior angles, which are and the unmarked angle (let’s call it ). So, .
Right Angle: The green marking indicates a right angle, which measures 90 degrees. Therefore, .
Substitution: Substitute into the equation from step 1: .
Solve for : Subtract from both sides of the equation: . Then, divide both sides by 2: .

Therefore,

Final Answer: The final answer is

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