Answer:
see explanation
Step-by-step explanation:
Diagram 1
The inscribed angle H is half the measure of its intercepted arc GI
The sum of the arcs on a circle is 360° , then
GI = 360° - HG - HI = 360° - 106° - 95° = 159° , so
∠ H = [tex]\frac{1}{2}[/tex] × HI = [tex]\frac{1}{2}[/tex] × 159° = 79.5°
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Diagram 2
∠ H = [tex]\frac{1}{2}[/tex] × UV = [tex]\frac{1}{2}[/tex] × 162° = 81°
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Diagram 3
The intercepted arc EF is twice the inscribed angle D
EF = 2 × 50° = 100°
DE is a diameter of the circle , then arc CD = 180° and
DF + EF = 180°
DF + 100° = 180° ( subtract 100° from both sides )
DF = 80°
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Diagram 4
If two chords of a circle are congruent (equal ) , then the corresponding arcs are congruent.
chord UV = chord ST , then arc UV = arc ST , so
UV = 82°
