Answer :

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°

-----------------------------------------------------------------------

Diagram 2

∠ H = [tex]\frac{1}{2}[/tex] × UV = [tex]\frac{1}{2}[/tex] × 162° = 81°

---------------------------------------------------------------------------

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°

-------------------------------------------------------------------------------

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°