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Answer:
When x = 22 the lines a and b are parallel lines cut by transversal f.
Step-by-step explanation:
Given : Measure of ∠CEF = 96° and measure of ∠HGB = (6x -36)°
We have to find the value of x so line a and b are parallel lines cut by transversal f.
Consider the given figure (we have renamed it as shown below)
Since, ∠CEF = 96°
Therefore, ∠AEG = 96° (vertically opposite angles)
Also for line a and b to be parallel the measure of angle ∠HGB and ∠AEG must be equal , then they form a pair of corresponding angles.
∠HGB = ∠AEG
(6x -36)° = 96°
adding 36 both side, we have ,
6x = 96 + 36
6x = 132
Divide both side by 6, we have,
x = 22
Thus, when x = 22 the lines a and b are parallel lines cut by transversal f.
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Rewritten by : Barada
Opposite exterior angles are congruent, so we can equate their measures and solve for x.
... 6x - 36 = 96
... x - 6 = 16 . . . . . . divide by 6
... x = 22 . . . . . . . . add 6
The value of x must be 22.
