Question

Identify the measure of arc RT. HELP ASAP!

Answer 1

35

Explanation:

I have no idea why I get these things right just by guessing but i do. I have no idea why, it was just right, lol

Answer 2

The correct option is;

RT = 35°

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.