Question

please answer this question it's my hw and i have to send to my mam. its urgent.​ please explain it step wise step

Answer 1

Given -

• ABCD is a cyclic quadrilateral in which AC and BD are its diagonals.

• ∠BAC=50°

• ∠CBD=65°

To find-

• ∠BCD=?

Solution -

For chord CD,

∠CBD= ∠CAD[Angle in the same segment are equal]

Therefore, ∠CAD=65°

Now,

=>∠BAD= ∠BAC + ∠CAD

=> ∠BAD= 50°+ 65°

=> ∠BAD= 115°

Now,

We know that,

Sum of opposite angles of a cyclic quadrilateral is 180°

Therefore,

=> ∠BAD+∠BCD= 180°

=> 115°+ ∠BCD=180°

=> ∠BCD=180°-115°

=> ∠BCD= 65°

$\boxed{\boxed{{\bf \: \therefore \: The \: value \: of \: ∠BCD = {65}^{0} }}}$