Answer:
The correct option is;
RT = 35°
Step-by-step explanation:
Given the parameters are;
∠SMX = 95°
∠MXS = 45°
arc PW = 80°
arc WY = 35°
From external angle half difference formula, we hve;
Given an external angle, ∠MSX, subtending a far arc x° and a near arc y°, then we have;
∠MSX = 1/2×(x° - y°)
Where:
x° = arc PW + arc WY = 80° + 35° = 115°
y° = arc RT
∠MSX + ∠SMX + ∠MXS = 180° (Sum of interior angles in a triangle)
∠MSX = 180° - (∠SMX + ∠MXS) = 180° - (95° + 45°) = 40°
Therefore;
∠MSX = 1/2×(x° - y°) gives;
40° = 1/2×(115 - y°)
y° = 115° - 2 × 40° = 35°
∴y° = 35° = arc RT.
