Answer:
The measure of ∠SVT is 79°
Step-by-step explanation:
In the given figure
∵ US ∩ RT at V
∴ ∠SVT and ∠UVR are vertically opposite angles
∵ The vertically opposite angles are equal in measures
∴ m∠SVT = m∠UVR
∵ m∠SVT = (5y + 9)°
∵ m∠UVR = (8y - 33)°
→ Equate them
∴ 8y - 33 = 5y + 9
→ Add 33 to both sides
∴ 8y - 33 + 33 = 5y + 9 + 33
∴ 8y = 5y + 42
→ Subtract 5y from both sides
∴ 8y - 5y = 5y - 5y + 42
∴ 3y = 42
→ Divide both sides by 3
∵ [tex]\frac{3y}{3}[/tex] = [tex]\frac{42}{3}[/tex]
∴ y = 14
→ Substitute the value of y in the measure of ∠SVT
∵ m∠SVT = 5(14) + 9
∴ m∠SVT = 70 + 9
∴ m∠SVT = 79°
∴ The measure of ∠SVT is 79°
