What is the measure of dg? in circle d, mgec is 230 degrees what is the measure of gdc? what is the measure of ac? segment co is congruent to segment hz which congruence statement is true? a. oz is congruent to co b. ch is congruent to coz c. ch is congruent to hzo d. co is congruent to hz in circle k, what is the value of x? a. x=30 b. x=25 c. x=20 d. x=15

Problem 1)

Minor arc DG is 110 degrees because we double the inscribed angle (DHG) to get 2*55 = 110

110 degrees



Problem 2)

Central angle GDC is the same measure as arc GFC. The central angle cuts off this arc.

The arcs GEC and GFC both combine to form a full circle. There are no gaps or overlapping portions.

So they must add to 360 degrees

(arc GEC) + (arc GFC) = 360
(230) + (arc GFC) = 360
(230) + (arc GFC)-230 = 360-230
arc GCF = 130 

130 degrees



Problem 3)

Similar to problem 1, we have another inscribed angle. ABC is the inscribed angle that cuts off minor arc AC

So by the inscribed angle theorem
arc AC = 2*(inscribed angle ABC)
3x+9 = 2*(3x-1.5)

Solve for x
3x+9 = 2*(3x-1.5)
3x+9 = 6x-3
9+3 = 6x-3x
12 = 3x
3x = 12
3x/3 = 12/3
x = 4

If x = 4, then 
arc AC = 3x+9
arc AC = 3*4+9
arc AC = 21

21 degrees



Problem 4)

Since we have congruent chords, this means that the subtended arcs are congruent. In this case, the arcs in question are CO and HZ

So arc CO is congruent to arc HZ

Answer is choice D



Problem 5)

We have a right triangle due to Thale's theorem

The angles 75 degrees and x degrees are complementary angles. They must add to 90

x+75 = 90
x+75-75 = 90-75
x = 15

Choice D) 15