Question

Choose the correct answer from the alternatives given.
In the below figure, AB || CD. If $\angle$DCE = x and $\angle$ABE = y then $\angle$CEB is equal to

• A. y - x
• B. $\frac{x+y)1}{2}$
• C. x + y - $\left(\frac{\pi }{2}\right)$
• D. x + y - $\pi$

Answer 1

The correct option is D x + y - $\pi$

$\angle$ CMB = $\angle$ DCM = x (Alternate interior angle)
$\angle$ BME = 180 - x; $\angle$ MBE = 180 - y

In $\Delta$ BME,

$\angle$ CEB = 180-[(180 - x) +(180-y)]

(Angle sum property of a triangle)
$\angle$ CEB = x + y - $\pi$