Question

Find STV
A. 39

B. 40

C. 45

D. 35

Answer 1

D. 35°.

Explanation:

1. additional building is performed and provided in the attachment;

2. m∠SUV=55/2x=27.5x;

3. m∠TUS=180-m∠SUV=180-27.5x;

4. m∠SUC=0.5(180°-95°)=42.5°, then m∠SUC=m∠CSU=42.5°;

5. m∠UST=90-m∠CSU=90-42.5=47.5°;

6. in ΔSTU: m∠UST+m∠TUS+m∠STU=180°, then

47.5°+180°-27.5x+10x+5°=180, ⇒ x=3;

7. finally, if x=3, then m∠STU=m∠STV=3*10+5=35°.