Answer:
m∠JTS = 104° ⇒ (A)
Step-by-step explanation:
The measure of an exterior angle of a triangle at one of its vertices equals the sum of the measures of the opposite interior angles.
Let us use this fact to solve the question
In ΔTSR
∵ T ∈ ray RJ
∴ ∠JTS is an exterior angle of ΔTSR
→ By using the fact above
∴ ∠TSR and ∠TRS are the opposite interior angles to ∠JTS
∴ m∠JTS = m∠TSR + m∠TRS
∵ m∠JTS = 27x - 4
∵ m∠ TSR = 30°
∵ m∠TRS = 18x + 2
→ Substitute their values in the equation above
∴ 27x - 4 = 30 + 18x + 2
→ Add the like terms in the right side
∴ 27x - 4 = 18x + 32
→ Add 4 to both sides
∴ 27x = 18x + 36
→ Subtract 18x from both sides
∴ 9x = 36
→ Divide both sides by 9
∴ x = 4
→ To find m∠JTS substitute x by 4 in its measure
∴ m∠JTS = 27(4) - 4 = 108 - 4
∴ m∠JTS = 104°
