In the figure: lines AB and CD intersect at O. 

If ∠ AOC + ∠ BOE = 70⁰ and ∠ BOD = 40⁰, find ∠ BOE and reflex ∠ COE.

 

 

 

In the figure, lines XY and MN intersect at O. If ∠POY = 90⁰ and a: b = 2: 3, find c.

                                                      

In the figure, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠ PRT.

 

 

In the figure, if x + y = w + z, then prove that AOB is a line.

                                                 

 

In the figure, POQ is a line. Ray OR is perpendicular to line PQ.

OS is another ray lying between rays OP and OR.

Prove that ∠ROS =

 

It is given that ∠ XYZ = 64⁰ and XY is produced to point P.

Draw a figure from the given information.

If ray YQ bisects ∠ ZYP, find ∠ XYQ and reflex ∠QYP.

In the figure, find the values of x and y and then show that AB || CD.

                                                       

In the figure, if AB || CD, CD || EF and y: z = 3: 7, find x.

                                                      

 

In the figure, if AB || CD, EF ⊥ CD and ∠GED = 126°. Find ∠ AGE, ∠GEF and ∠FGE.

 

 

In the figure, if PQ || ST, ∠PQR = 110⁰ and ∠ RST = 130⁰, find ∠QRS.

 

 

In the figure, if AB || CD, ∠APQ = 50⁰ and ∠PRD = 127°, find x and y.

 

 

In the figure, PQ and RS are two mirrors placed parallel to each other.

An incident ray AB strikes the mirror PQ at B, the reflected ray moves along

the path BC and strikes the mirror RS at C and again reflects back along CD.

Prove that AB || CD.

 

 

In the figure, sides QP and RQ of ∆ PQR are produced to points S and T respectively.

If ∠SPR = 135⁰ and ∠PQT = 110⁰, find ∠PRQ.

 

 

 

In the figure, ∠ X = 62⁰, ∠ XYZ = 54⁰.

If YO and ZO are the bisectors of ∠ XYZ and ∠ XZY respectively of ∆ XYZ, find ∠OZY and ∠YOZ.

 

 

 

In the figure, if AB || DE, ∠ BAC = 35⁰and ∠CDE = 53⁰, find ∠ DCE.

 

 

 

 

In the figure, if lines PQ and RS intersection point T,

such that ∠ PRT = 40⁰, ∠RPT = 95⁰ and ∠TSQ = 75⁰, find ∠SQT.

 

 

In the figure, if PT ⊥ PS, PQ || SR, ∠SQR = 28⁰ and ∠QRT = 65⁰, then find the values of x and y.

 

 

In the figure, the side QR of ∆PQR is produced to a point S.

If the bisectors of ∠PQR and ∠ PRS meet at point T, then prove that ∠QTR = .