Question

The bisectors of angle A and Angle B meet at a point O. If angle C = 100 degree and Angle D equal to 50 degree find angle AOB ..
Please answer quickly its of 15 Marks ​

Answer 1

Answer:

thanks for your question about the following to show you the answer ,the answer is 75

Answer 2

SOLUTION

We know that, sum of all four angles of quadrilateral is 360°.

∠A + ∠B +∠C +∠D =360°

=)∠A+ ∠B + 100°+50°=360°

=)∠A+ ∠B+ 150°= 360°

=)∠A +∠B= 360°-150°

=)∠A+ ∠B= 210°

Now, according to question bisector of ∠A & ∠B meet in a point P and forms the ∆PAB.

So,

1/2∠A+ 1/2∠B= 210°/2

=) 105°

As we know that, sum of all angles of ∆ is 180°.

∠ABO + ∠BAO + ∠AOB= 180°

=)1/2∠A + 1/2∠B + ∠AOB= 180°

=) 105° + ∠AOB= 180°

=) ∠AOB= 180° -105°

=) ∠AOB= 75°

Hope it helps ☺️