When two lines are parallel and they cut by the transversal, the following pairs will be congruent.
Sum of consecutive interior angles on the same side of the transversal will be equal to 180 degree.
Find the angle x in the figure given below. Give your reason.
Example 1 :
Solution :
∠ACB = ∠CFE
Because they are corresponding angles.
So,
x = 125
Example 2 :
Solution :
∠BCF = ∠CFG
Because they are alternate angles.
So,
x = 57
Example 3 :
Solution :
∠EFH = ∠CFG
Because they are vertically opposite angles.
So,
x = 70
Example 4 :
Solution :
∠DCH = ∠CFG
Sum of consecutive interior angle is 180.
x + 105 = 180
x = 180 - 105
x = 75
Example 5 :
Solution :
∠DCF = ∠EFH
∠DCF = 53
∠CFE + ∠EFH = 180
53 + x = 180
x = 180 - 53
x = 127
Example 6 :
Solution :
∠BCA = ∠DCF (Vertically opposite angles)
∠CFG = ∠EFH (Vertically opposite angles)
∠EFA = ∠BCA = x (Corresponding angles)
∠HFE + ∠EFA = 180
133 + x = 180
x = 180 - 133
x = 47
Example 7 :
Are the lines AB and CD parallel? Explain your answer.
Solution :
By adding the interior angles ,
= ∠BAC + ∠DCA
= 72 + 108
= 180
The sum of interior angles is 180 degree, the angles involving here are parallel.
Example 8 :
Find the missing angle. Give reasons for your answer
Solution :
Triangle ECD is isosceles triangle.
∠CED + ∠EDC + ∠DCE = 180
∠EDC = ∠DCE
40 + ∠EDC + ∠EDC = 180
Subtract 40 on both sides.
2∠EDC = 180 - 40
2∠EDC = 140
Divide by 2 on both sides.
∠EDC = 70
∠ECD = 70
∠CEF = x
x = 70 (Alternate interior angles)
Example 9 :
Find x.
Solution :
5x - 10 = 4x + 15
(Alternate exterior angles)
Subtract 4x on both sides.
5x - 4x - 10 = 15
Add 10 on both sides.
x = 15 + 10
x = 25
Example 10 :
Find x.
Solution :
The angles involving in the problem given above is consecutive interior angles on the same side of the transversal.
x + 22 + 2x - 13 = 180
3x + 9 = 180
3x = 180 - 9
3x = 171
x = 171/3
x = 57
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