The values of x are 16 and 11 then the measure of the arc will be marc DE = 167°, marc EF = 13°, marc DFG = 347°, marc MN = 65°, marc NP = 115°, and marc NQP = 245°.
Angle is the space between the line or the surface that meets. And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
The angle ∠EFH and ∠HFG are supplement angles. Then we have
∠EFH + ∠HFG = 180
x - 3 + 12x - 25 = 180
13x = 180 + 28
x = 16
The measure of the arc will be given as
marc DE = 167°
marc EF = 13°
marc DFG = 347°
The angle ∠MRN and ∠PRQ are vertically opposite angles. Then we have
∠EFH = ∠HFG
10x - 45 = 6x - 1
4x = 44
x = 11
The measure of the arc will be given as
marc MN = 65°
marc NP = 115°
marc NQP = 245°
More about the angled link is given below.
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