Question

7.
In A ABC, bisectors of ZA and B intersect at point o. If ZC = 70°. Find measure
of ZAOB​

Answer 1

Answer:

∠AOB = 125°. Please mark me as brainliest.

Step-by-step explanation:

Please draw a figure for reference.

∠A + ∠B + ∠C = 180° (Triangle angle sum property)

(∠A + ∠B) + 70° = 180°

∠A + ∠B = 110°   (Eqn. 1)

Now, ∠OAB + ∠OBA + ∠AOB = 180° (Triangle angle sum property)

But, ∠OAB = 1/2 ∠A (As OA is angle bisector)

And, ∠OBA = 1/2 ∠B (As OB is angle bisector)

So, 1/2 ∠A + 1/2 ∠B + ∠AOB = 180°

1/2 (∠A + ∠B) + ∠AOB = 180°

1/2 (110°) + ∠AOB = 180° (from 1)

55° + ∠AOB = 180°

∠AOB = 125°