Question

plz answer it fast! tommorow is my exam .


In the fig, L ll m. bisectors of angle RQB and angle DRQ intersect at P. find the measure of angle RPQ .

Answer 1

Since the line L and M are Parallel....

Therefore, the co interior angles are suplementry...

<DRP + <BQR = 180°

On dividing both sides by 2, we get

=> (<DRP/2 ) + (<BQR /2) = 90°

=> <1 + <3 = 90° -------(1)

Now, In Triangle RPQ

By angle sum property of triangle

<1 + <3 + <RPQ = 180

=> 90 + <RPQ = 180

=> <RPQ = 90°

Answer 2

ang. RQB + DRQ = 180
1/2 RQB + 1/2 DRQ = 1/2 (180)
ang. PRQ + PQR =90
Now, in tri. PQR
ang. (PQR + PRQ) + RPQ = 180
[ since. PQR + PRQ =90]
therefore, 90+ RPQ = 180
RPQ = 180 -90
RPQ = 90