Question

TV−→− bisects ∠STU, m∠STV=(14x+8)∘, and m∠UTV=(x+2)∘. Find m∠STU

Answer 1

m∠STU is 20°

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 =
`(1)/(2)` m∠STU

∵ m∠STV = (
`(1)/(4)`x + 8)°

∴ m∠UTV = (x + 2)°

→ Equate them

∴ x + 2 =
`(1)/(4)`x + 8

→ Subtract 2 from both sides

∴ x + 2 - 2 =
`(1)/(4)`x + 8 - 2

∴ x =
`(1)/(4)`x + 6

→ Subtract
`(1)/(4)`x from both sides

∴ x -
`(1)/(4)`x =
`(1)/(4)`x -
`(1)/(4)`x + 6

∴
`(3)/(4)`x = 6

→ Divide both sides by
`(3)/(4)` to find x

∴ x = 8

→ Substitute the value of x in the measure of any given angle

∵ m∠UTV = 8 + 2 = 10°

∵ m∠UTV =
`(1)/(2)` m∠STU

∴ 10° =
`(1)/(2)` m∠STU

→ Multiply both sides by 2

∴ 20° = m∠STU

∴ The measure of angle STU is 20°