Q. 54.3( 330 Votes )

# In Fig. 6.32, if AB || CD, ∠ APQ = 50° and∠ PRD = 127°, find x and y.

Answer :

It is given in the question that:

AB parallel CD,

∠APQ = 50^{o} and,

∠PRD = 127^{o}

According to question,

x = 50^{o} (Alternate interior angle)

∠PRD + ∠PRQ = 180^{o} (Angles on the straight line are supplementary)

127^{o} + ∠PRQ = 180^{o}

∠PRQ = 53^{o}

Now,

In Δ PQR,x + y + ∠PRQ = 180

^{o }(Sum of interior angles of a triangle)

y + 50^{o} + ∠ PRQ = 180^{o}

y + 50^{o} + 53^{o} = 180^{o}

y + 103^{o} = 180^{o}

y = 77^{o}

Rate this question :

In the given figure, AB || CD. If ∠ABO = 130° and ∠OCD = 110°, then ∠BOC = ?

RS Aggarwal & V Aggarwal - Mathematics

In Fig 8.106, *l, m* and *n* are parallel lines intersected by transversal *p* at *X, Y* and and *Z* respectively. Find ∠1, ∠2 and∠3.

RD Sharma - Mathematics

In Fig 8.117, *p* is a transversal to lines *m* and *n*, ∠2 = 120° and ∠5 = 60°. Prove that *m*||*n*.

RD Sharma - Mathematics

In Fig 8.116, if *l||m||n* and ∠1 = 60°, find ∠2

RD Sharma - Mathematics

In Fig. 8.136, if *CP* || *DQ*, then the measure of *x* is

RD Sharma - Mathematics

In Fig. 8.142, if lines *l* and *m* are parallel, then the value of *x* is

RD Sharma - Mathematics

In Fig. 8.138, if lines *l* and *m* are parallel, then *x* =

RD Sharma - Mathematics

In Fig. 8.137, if *AB*|| *HF* and *DE*||*FG*, then the measure of ∠*FDE* is

RD Sharma - Mathematics

In Fig. 8.132, if *l*_{1} || *l*_{2}, what is the value of *y*?

RD Sharma - Mathematics