Question

What is mZSVT? Enter your answer in the box.

Answer 1

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

∵ $\frac{3y}{3}$ = $\frac{42}{3}$

∴ 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°