Question

(TV) ⃗ bisects ∠STU, m∠STV = (4/5 x 10)°, m∠UTV = (x-3)°. Find m∠STU.

A) (4/5 x 10)°
B) (x-3)°
C) (8/5 x 10)°
D) (2x-6)°

Answer 1

To find m∠STU, we first equate the given angles because ⟡TV bisects ∠STV, then solve for x and use the value of x to calculate the full angle.

Step-by-step explanation:

To solve for m∠STU when ∠STV is bisected by vector ⟡TV, we have that m∠STV = (4/5 × 10)° and m∠UTV = (x - 3)°. Since ⟡TV is the bisector, m∠STV should be equal to m∠UTV.

Therefore, we set up an equation with the given angle measures:

• (4/5 × 10)° = (x - 3)°

Simplifying the equation gives us:

• 8° = (x - 3)°
• x = 8° + 3°
• x = 11°

Now, to find m∠STU, we add the measures of m∠STV and m∠UTV, which are equal:

• m∠STU = 2 × (4/5 × 10)°
• m∠STU = 2 × 8°
• m∠STU = 16°

Hence, m∠STU is equal to (8/5 × 10)°, which indicates that the correct answer is Option C).