Answer:
m∠STU = (5/4)x +10°
m∠STU = 20°
Explanation:
Given:
m∠STV = ((1/4)x+8)°
m∠UTV = (x+2)°
Since line TV bisects ∠STU, then;
m∠STV = m∠UTV
Substituting their values;
((1/4)x +8)° = (x+2)°
Collecting the like terms.
(1/4)x - x = 2 - 8
(-3/4)x = -6°
x = -6 × -4/3
x = 8°
Since,
m∠STU = m∠STV + m∠UTV
m∠STU = ((1/4)x+8)° + (x+2)°
m∠STU = (5/4)x +10
Substituting the value of x;
m∠STU = (5/4)(8°) +10°
m∠STU = 10° + 10° = 20°
m∠STU = 20°