Question

Please ans the below fig.8.90
ABCD is a straight line. Find which angle is greater?
A) RB or RC?
B) PB or PR?
Plz ans fast

Answer 1

First of all draw a parallel line to ABCD
Name it WXYZ
angleABX=angleBXY
i.e=114=90+x
      114-90=x
      24 degrees=x

Now do the same thing for the next angle.
angleYCD+angleYCB=180 degrees
reason:linear pair
112+angleYCB=180 degrees
angleYCB=180-112
                 =68 degrees

angleXYC=angleYCD=112 degrees
i.e  112=90+x
      112-90=x
       22 degrees=x

angleYXR+angleXRY+angleRYX=180 degrees
reason:angle sum property of a triangle
24+angleXRY+22=180 degrees
angleXRY+46=180
angleXRY=180-46
angleXRY=134 degrees

Now next step is 
angleXRY+angleYRC=180 degrees
reason=linear pair
134+angleYRC=180 degrees
angleYRC=180-134
angleYRC=46 degrees

angleYRC+angleRCY+angleCYR=180 degrees
reason:angle sum property of triangle
46+angleRCY+90=180
angleRCY+136=180
angleRCY=180-136
angleRCY=44 degrees

angleYCD+angleYCR+angleRCB=180 degrees
reason:linear pair
112+44+angleRCB=180 degrees
angleRCB=180-156
angleRCB=24 degrees

angleXRY=angleBRC=134 degrees
reason:vertically opposite angles

angleRCB+angleBRC+angleRBC=180 degrees
reason:angle sum property of triangle
24+134+angleRBC=180 degrees
angleRBC=180-158
                 =22 degrees

Now
angleBXR=90 degrees
angleXRB=angleYRC=46 degrees
reason:vertically opposite angles
angleBXR+angleXRB+angleRBX=180 degrees
reason:angle sum property of triangle
90+46+angleRBX=180 degrees
angleRBX+136=180
angleRBX=180-136
                =44 degrees

Now we have all the angles so the answers for ur questions are as follows
i]angle RC is greater than RB
ii]angle PR is greater than PB
hope u understood the concept
I ask ur apology for giving u such big and lengthy answer if u didnt understood plz mail me on [email protected]

Thank u