Question

In figure AB is parallel to CD is parallel to EF and AE is parallel to BF. Find x,y,p,q and w ​

Answer 1

y=35 degree (alternate interior angles)

Answer 2

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We have,

$\implies$ AB parallel to CD and BF is transversal

$\therefore \: \angle\:ABD = \angle\: CDF$ [Corresponding Angles]

$\therefore \: {35}^{\circ} + {45}^{\circ} = \angle\: CDF$

or $\angle\:p = {80}^{\circ}$

Now,

$\implies$ CD is parallel to EF and DF is a transversal.

$\therefore \: \angle\:p + \angle\: q = {180}^{\circ}$ [Pair of Interior Angles on Same side of Transversal ]

$\therefore\: \angle\:q = {180}^{\circ} - {80}^{\circ}$

$\angle\:q = {100}^{\circ}$

Also,

$\implies$ AB is parallel to CD and BE is transversal

$\therefore\:\angle\:ABO = \angle\:BOD$ [alternate interior angles]

$\therefore\:\angle\:BOD = {35}^{\circ}$

$\angle\:x + \angle\:BOD = {180} ^{\circ}$ [Linear Pair]

$\therefore \angle\:x = {180}^{\circ} - {35}^{\circ} = {145}^{\circ}</p><p></p><p>[tex]\angle\:ABE = \angle\:y$ [Alternate Interior Angles ]

$\therefore\: \angle\:y = {35}^{\circ}$