Question

In the figure, AD and CE are the angle bisectors of angle A and Angle C respectively.If angle ABC = 90°, then find angle AOC.​

Answer 1

Answer:

Step-by-step explanation:

Let angle a = angle c

so, angle a = angle c = 45°

AD and CE are bisectors so angle OAC = angle OCA = 22.5°

So, angle AOC = 180°-(22.5+22.5)°

                          =180°-45°

                          =135°

HOPE IT HEPLS SOMEONE HERE !!!!!!!

Answer 2

Step-by-step explanation:

According to the question, it is given that, AD and CE are the angle bisectors of ∠A and ∠C respectively and ∠ABC=90∘ .

Now In △ABC, by angle sum property of triangles, we get

∠A+∠B+∠C=180∘

But it is given that ∠ABC=90∘, hence,

⇒∠A+90∘+∠C=180∘

⇒∠A+∠C=90∘……………………………..(1)

Now, in △AOC,

Again by angle sum property of triangles,

∠OAC+∠AOC+∠OCA=180∘…………………………….(2)

But, it is given that AD and CE are the angle bisectors of ∠A and ∠C respectively.

This means that they divide the angles ∠A and ∠C in two equal angles.

∴∠OAC=12∠A

Also, ∠OCA=12∠C

Hence, from equation (2), we get

12∠A+∠AOC+12∠C=180∘

⇒12(∠A+∠C)+∠AOC=180∘

Now, substituting ∠A+∠C=90∘ in the above equation, we get

⇒12(90∘)+∠AOC=180∘

⇒45∘+∠AOC=180∘

Solving further,

⇒∠AOC=180∘−45∘=135∘

Therefore,

the required value of ∠AOC=135∘