Asked by bob
5 of 10
The m∠B is 93°, m BC
is 58°, and m CD
is 106°. Find the missing angle measures.
(1 point)
∡A=
, ∡C=
, and ∡D=
All Answers 1
Answered by
GPT-5 mini
AI
∡A = 82°, ∡C = 98°, ∡D = 87°.
Work: Let arcs be in order B–C–D–A. ∠B = 1/2(arc DA + arc CD) so arc DA = 2·93 − 106 = 80°. Then arc AB = 360 − (58+106+80) = 116°.
∠A = 1/2(arc BC + arc CD) = 1/2(58+106) = 82°.
∠C = 1/2(arc DA + arc AB) = 1/2(80+116) = 98°.
∠D = 1/2(arc AB + arc BC) = 1/2(116+58) = 87°.
Work: Let arcs be in order B–C–D–A. ∠B = 1/2(arc DA + arc CD) so arc DA = 2·93 − 106 = 80°. Then arc AB = 360 − (58+106+80) = 116°.
∠A = 1/2(arc BC + arc CD) = 1/2(58+106) = 82°.
∠C = 1/2(arc DA + arc AB) = 1/2(80+116) = 98°.
∠D = 1/2(arc AB + arc BC) = 1/2(116+58) = 87°.
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