Question

in the figure, AB ||CD and CD ||EF. Also, EA |AB if angle BEF =55°,find the values of x, y and z.

Answer 1

As AE is a perpendicular to CD,AB,EF ;angle z + 55 = 90. So, angle z = 90 - 55 = 35 degrees

We have a statement that Sum of opposite interior angles of an one interior angle of a triangle is equal to the exterior angle of that interior angle. That means, Sum of angle BAC + angle z = angle x

 So, 90 + 35 = angle x
         angle x = 125 degrees.
 
As EB is a tnnasversal for AB & CD, angle x & angle y are corresponding angles. We know that corresponding angles are equal.

So, x = 125 degrees, y = 125 degrees & z = 35 degrees

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Answer 2

Correct question :- In the figure, AB ||CD and CD ||EF. Also, EA ⊥ AB if angle BEF = 55°, F ind the values of x, y and z.

$\huge\bf{Solution-}$

• Since corresponding angles are equal.

→ x = y

• We know that the that the interior angles on the same side of the transversal are 180.

→ y + 55 = 180°

→ 180° - 55° = 125°

So, x = y = 125°

• Since AB || CD and CD || EF.
• AB || EF

→ EAB + FEA = 180°

• [Interior angles on the same side of the transversal EA are supplementary.]

→ 90° + z + 55° = 180°

→ z = 35°