Question

In the given figure if ∠ATO=40°, find ∠AOB.

Answer 1

Answer:

100°

Step-by-step explanation:

line seg. OT splits angle ATB into two equal parts which are ATO and BTO

As we know angle ATO is 40° then, Angle BTO is the same

Therefore,Angle ATB is 80°

Now,OA and OB are radius of a circle joining tangents AT and BT

forming angles OBT and OAT respectively.

Therefore,these angles are right angles

Finally,A.S.P of Quadrilateral is sum of 4 angles makes 360°

Which on solving with the following values,we get:

Angle AOB is known to be 100°