(TV ) bisects ∠STU, m∠STV = (1/4 x+8)°, and m∠UTV = (x+2)°. Find m∠STU.

m∠STU = (5/4)x +10°

m∠STU = 20°

Step-by-step 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°

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