Question

please give me answer​

Answer 1

Given

• AB=CD
• ∠AOB=30°

To Find

• ∠OCD

Solution

$\sf \: Now \: in \: ∆AOB \: and \: ∆DOC \: We \: have,$

$\sf \: AB=CD \: \: \: \: \: \: \: (given)$

$\sf \: OA=OD \: \: \: \: \: (radius)$

$\sf \: OB=OC \: \: \: \: \: (radius)$

$\sf \: So \: by \: SSS \: criterion \: of \: congruence \: We \: have$

∆AOB ≅ ∆DOC

$\sf \: ∠AOB=∠DOC \: \: \: \: \: \: \: \: (cpct)$

$\\\\ \sf ∠DOC= 30°$

$\sf \: OD=OC \: \: \: \: \: (radius)$

• If Two line Are Equal then The Opposite Angle will be Equal

therefore ∠ODC=∠OCD

Now in ∆COD we have

$\sf →∠ODC+∠OCD+∠DOC= 180°. ~~~~~Angle\ Sum\ property$

$\sf →2∠OCD=180-30$

$\sf→2∠OCD=150$

$\sf ~~~~~~ ∠OCD=75°$