Find the Missing Angle in a Triangle with an Exterior Angle of 150 Degrees

Published on September 4, 2024

Question

what is the right angle?

Answer

Let’s approach this step-by-step:
  1. First, we need to understand what information we have:
    • There’s a triangle with one angle labeled as 25°
    • There’s an exterior angle labeled as 150°
    • We’re asked to find the angle labeled as X°
  2. Recall the exterior angle theorem:
    An exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
  3. In this case, 150° is the exterior angle, and it’s equal to the sum of 25° and X°.
  4. We can write this as an equation:
  5. To solve for X, we subtract 25° from both sides:

  6. Therefore, X = 125°
  7. To verify, we can check if the angles in the triangle add up to 180°:
    (The 30° angle is not labeled but can be deduced)
Thus, the angle X is 125°.
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