Answer:
m∠STU is 20°
Step-by-step explanation:
If a ray bisects an angle, then it divides it into two equal angles in measures and the measure of each one is half the measure of this angle
∵ Ray TV bisects ∠STU
→ That means it divides it into two angles STV and UTV
∴ m∠STV = m∠UTV = [tex]\frac{1}{2}[/tex] m∠STU
∵ m∠STV = ([tex]\frac{1}{4}[/tex]x + 8)°
∴ m∠UTV = (x + 2)°
→ Equate them
∴ x + 2 = [tex]\frac{1}{4}[/tex]x + 8
→ Subtract 2 from both sides
∴ x + 2 - 2 = [tex]\frac{1}{4}[/tex]x + 8 - 2
∴ x = [tex]\frac{1}{4}[/tex]x + 6
→ Subtract [tex]\frac{1}{4}[/tex]x from both sides
∴ x - [tex]\frac{1}{4}[/tex]x = [tex]\frac{1}{4}[/tex]x - [tex]\frac{1}{4}[/tex]x + 6
∴ [tex]\frac{3}{4}[/tex]x = 6
→ Divide both sides by [tex]\frac{3}{4}[/tex] to find x
∴ x = 8
→ Substitute the value of x in the measure of any given angle
∵ m∠UTV = 8 + 2 = 10°
∵ m∠UTV = [tex]\frac{1}{2}[/tex] m∠STU
∴ 10° = [tex]\frac{1}{2}[/tex] m∠STU
→ Multiply both sides by 2
∴ 20° = m∠STU
∴ The measure of angle STU is 20°
