Question

Question #2
Find the measure of UK
T
99
O
U
87 R
S
K

Answer 1

UK = 75°

Explanation:

the measure of the chord- chord angle TRS is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

∠ TRS =
`(1)/(2)` (TS + UK) , that is

87° =
`(1)/(2)` (99 + UK) ← multiply both sides by 2 to clear the fraction

174° = 99° + UK ( subtract 99° from both sides )

75° = UK