Question

What is the Answer? Geometry

Answer 1

∠ SUT = 41.5°

Explanation:

if ∠ SUT was the central angle , that is the angle at the centre of the angle then it would equal the chord that subtends it.

However, ∠ SUT is not the central angle subtended by arc ST , thus

∠ SUT ≠ ST

∠ SUT is a chord- chord angle and is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

∠ SUT =
`(1)/(2)` (ST + QR) =
`(1)/(2)` ( 46 + 37)° =
`(1)/(2)` × 83° = 41.5°