Find x,y and z from the given figure, if AB ǁ CD.
Answers
Answer:
Given, AB∣∣CD,
Consider AC is transversal.
z=125
o
[∵ Corresponding angles ]
x=180−125
o
[ ∵ sum of angles in a straight line=180
o
]
x=55
o
We know that, sum of all the interior angles in a quadrilateral is 360
o
∠A+∠B+∠C+∠D
x+x+z+y=360
o
55+55+125+y=360
o
⟹y=125
Solution:-
It is given that AB || CD and EF is a transversal From the figure we know that ∠AEF and ∠EFG are alternate angles So we get ∠AEF = ∠EFG = 75o ∠EFG = y = 75o
From the figure we know that ∠EFC and ∠EFG form a linear pair of angles
So we get ∠EFC + ∠EFG = 180o It can also be written as x + y = 180o
By substituting the value of y we get x + 75o = 180o
On further calculation we get x = 180o – 75o By subtraction x = 105o
From the figure based on the exterior angle property it can be written as ∠EGD = ∠EFG + ∠FEG
By substituting the values in the above equation we get 125o = y + z 125o = 75o + z
On further calculation we get z = 125o – 75o By subtraction z = 50o
Therefore, the values of x, y and z are 105o, 75o and 50o.