Answer:
u = 24
Explanation:
Exterior Angle Theorem
The interior angles of a triangle sum to 180°. Angles on a straight line sum to 180°. Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.
From inspection of the triangle:
- Exterior angle = 5u
- Non-adjacent interior angle = 2u
- Non-adjacent interior angle = 2u + 24
Therefore:
⇒ 5u = (2u + 24) + 2u
⇒ 5u = 2u + 24 + 2u
⇒ 5u = 4u + 24
Subtract 4u from both sides:
⇒ 5u - 4u = 4u + 24 - 4u
⇒ u = 24
Therefore, the value of u is 24.