Question

in abc right angled at b from the other two angles one angle is twice of the other angle the bisector of right angle and the larger acute angle meet at a point o then find the angle between two bisector​

Answer 1

Answer:

We know that the sum of all three angles of a triangle is 180 ∘ .

Hence, for △ABC, we can say that:

∠A+∠B+∠C=180 ∘

⇒∠A+90 ∘ +∠C=180 ∘

⇒∠A+∠C=90 ∘

For △OAC:

∠OAC= 2

∠A

[OA bisects ∠A]

∠OCA= 2

∠C

[OC bisects ∠C]

On applying the abive logic to △OAC, we get

∠AOC+∠OAC+∠OCA=180 ∘

[Sum of angles of △AOC]

⇒∠AOC+ 2

∠A + 2∠C =180°

⇒∠AOC+ 2

∠A+∠C =180 ∘

⇒∠AOC+ 290 =180 ∘

[∵∠A+∠C=90 ° ]

⇒∠AOC=180 ∘ −45 °

⇒∠AOC=135 ∘

maaf kalo salah