Question

in the figure ABIICD and CDIIEF Also EAit is perpendicular bisector of AB if angleBEF is equal to 55 degree find the value of X Y and Z

Answer 1

Given, AB।। CD
and BE is the transversal
So,
x=y (corresponding angles)........(i)

Also,
CD।।EF and BE is transversal
so,
y + 55 degree = 180 degree
(interior angles of the same side of the transversal are supplementary)

=> y = (180-55) degree

=>y = 125 degree

From (i)
x = y
x = 125 degree

Also,
EF।।AB
and AE is transversal

So,
angle BAE + angle FEA = 180 degree
(interior angles on the same side of the transversal are supplementary)

=>90 degree + ( z + 55 degree) = 180 degree

=>55 degree + 90 degree + z = 180 degree

=> 145 degree + z = 180 degree

=> z = 35 degree

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