We are given a geometric figure involving a triangle and an angle outside the triangle. Let's analyze it step by step.
Given:
- A triangle $ \triangle TSU $
- Point $ S $ lies on a straight line with point $ F $, forming a straight angle at $ S $
- $ \angle T = 65^\circ $
- $ \angle FST = 105^\circ $ (this is the angle between the extension of $ SU $ and $ TS $)
- We are to find $ \angle U $, which is marked as "?"
- Multiple choice:
A) 35°
B) 75°
C) 40°
D) 36°
---
Step 1: Understand the configuration
We have a triangle $ \triangle TSU $, with:
- Point $ F $ lying on the extension of $ SU $ beyond $ S $, so that $ F-S-U $ is a straight line.
- So, $ \angle FST = 105^\circ $ is the
exterior angle at vertex $ S $, formed between side $ TS $ and the extension $ FS $.
This means that $ \angle TSU $, the
interior angle at $ S $ in triangle $ TSU $, is supplementary to $ \angle FST $, because they form a straight line.
So:
$$
\angle TSU = 180^\circ - 105^\circ = 75^\circ
$$
---
Step 2: Use triangle angle sum
In triangle $ TSU $, we now know two angles:
- $ \angle T = 65^\circ $
- $ \angle S = 75^\circ $
The sum of angles in any triangle is $ 180^\circ $. So:
$$
\angle U = 180^\circ - \angle T - \angle S = 180^\circ - 65^\circ - 75^\circ = 40^\circ
$$
---
Final Answer:
$$
\boxed{C) \ 40^\circ}
$$
✔ Answer: C) 40°
Parent Tip: Review the logic above to help your child master the concept of exterior angle inequality theorem worksheet.
