Question

Circle D is shown. Line segments D E, D F, D G, and D H are radii. Angle E D F is 55 degrees, angle F D G is 70 degrees, and angle G D H is 110 degrees.
Which arc is congruent to Arc E H?

Arc G H
Arc F H
Arc G E
Arc F G

Answer 1

Answer:

see the explanation

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of arc EH

Remember that the measure of the complete circle is equal to 360 degrees

so

$arc\ EH+arc\ EF+arc\ FG+arc\ GH=360^o$

Remember that

$arc\ EF=m\angle EDF$ ----> by central angle

$arc\ FG=m\angle FDG$ ----> by central angle

$arc\ GH=m\angle GDH$ ---> by central angle

substitute the given values

$arc\ EH+55^o+70^o+110^o=360^o$

$arc\ EH=360^o-235^o=125^o$

step 2

Which arc is congruent to Arc E H?

we know that

$arc\ EFG=arc\ EF+arc\ FG=55^o+70^o=125^o$

therefore

arc EH is congruent with arc EFG

or

arc EH is congruent with minor arc GE

Answer 2

Answer:

its c arc GE

Step-by-step explanation: