Let -OX be a ray and let -OA and -OB be two rays on the same side of -OX- with -OA between -OX and -OB- Let -OC be the bisector of - AOB- Prove that - XOA - - XOB - 2- XOC-

OC is bisector of AOB ∴∠ BOC=∠ AOC=x #176; To proof ∠ XOA+∠ XOB=2∠ XOC L.H.S ∠ XOA+∠ XOA+∠ AOB ⟹ 2∠ XOA+2∠ AOC ⟹ 2(∠ ...

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Byju's Answer

Standard VI

Mathematics

Collinear Points

Let →OX be ...

Question

Let $\to O X$ be a ray and let $\to O A$ and $\to O B$ be two rays on the same side of $\to O X$ , with $\to O A$ between $\to O X$ and $\to O B$ . Let $\to O C$ be the bisector of $∠ A O B$ . Prove that $∠ X O A + ∠ X O B = 2 ∠ X O C$ .

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Solution

$O C$ is bisector of $A O B$
$∴ ∠ B O C = ∠ A O C = x °$
To proof $∠ X O A + ∠ X O B = 2 ∠ X O C$
$L . H . S$
$∠ X O A + ∠ X O A + ∠ A O B$
$⟹ 2 ∠ X O A + 2 ∠ A O C$
$⟹ 2 (∠ X O A + ∠ A O C)$
$⟹ 2 ∠ X O C$ $(R . H . S)$ $(P r o v e d)$

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Let →OX be a ray and let→OA and →OB be two rays on the same side of →OX, with →OA between →OX and →OB. Let →OC be the bisector of ∠AOB. Prove that ∠XOA+∠XOB=2∠XOC.

OC is bisector of AOB∴∠BOC=∠AOC=x°To proof ∠XOA+∠XOB=2∠XOCL.H.S∠XOA+∠XOA+∠AOB⟹2∠XOA+2∠AOC⟹2(∠XOA+∠AOC)⟹2∠XOC (R.H.S) (Proved)

Let $\to O X$ be a ray and let $\to O A$ and $\to O B$ be two rays on the same side of $\to O X$ , with $\to O A$ between $\to O X$ and $\to O B$ . Let $\to O C$ be the bisector of $∠ A O B$ . Prove that $∠ X O A + ∠ X O B = 2 ∠ X O C$ .

$O C$ is bisector of $A O B$
$∴ ∠ B O C = ∠ A O C = x °$
To proof $∠ X O A + ∠ X O B = 2 ∠ X O C$
$L . H . S$
$∠ X O A + ∠ X O A + ∠ A O B$
$⟹ 2 ∠ X O A + 2 ∠ A O C$
$⟹ 2 (∠ X O A + ∠ A O C)$
$⟹ 2 ∠ X O C$ $(R . H . S)$ $(P r o v e d)$