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Step-by-step explanation:

for 2 lines to be parallel they must have the same angles with a crossing third line.

and it is a given for 2 crossing lines that the

top right angle = bottom left angle

top left angle = bottom right angle

it is also clear that the sum of all angles around a single point in one side of a line must be 180° (as the line is the diameter of a potential circle with the single point being the center of that circle, and so one side of the line represents a half-circle = 180°).

7.

angle 3 plus angle 8 are together 180°.

66 + 2x + 8 = 180

2x + 8 = 114

2x = 106

x = 53

8.

3x + 48 = 6x

48 = 3x

x = 16

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh