Question

Please give me the answers of question number 9 (fig 2)​

Answer 1

Answer:

Since it is a quadrilateral so sum of all angles is 360°

Now Angles A+B+C+D=360°

A+B+50°+100°=360°

from here we get, A+B=360°-150°=210°

as angle PAB and angle PBA are the bisectors of angle A and B

Hence, angle PAB + angle PBA= 1/2 Of 210°=105°

Now on applying angle sum property in triangle PAB, Angle PAB+ PBA+ APB=180°

or 105°+APB=180°

You get APB=75°

The short method of this is if the bisectors of any two angles meet at a point inside a quadrilateral then the angle made by the bisectors=1/2 of the two remaining angles of quadrilateral

In this fig angle APB=1/2 of C+D= 1/2×150°=75°