MathematicsIn figure, D is cyclic quadrilateral in which AC and BD are diagonals. If ∠DBC=550and ∠BAC=450, then which of the following is the measure of ∠BCD?

In figure, $D$ is cyclic quadrilateral in which $AC$ and $BD$ are diagonals. If $∠ DBC = 55^{0}$ and $∠ BAC = 45^{0}$ , then which of the following is the measure of $∠ BCD$ ?

A
$80^{0}$
B
$90^{0}$
C
$110^{0}$
D
$115^{0}$

Solution:

Consider the given figure,

From the figure-

D

is cyclic quadrilateral in which

AC

and

BD

are diagonals.

∠ DBC = 55^{0}

and

∠ BAC = 45^{0}

.
Here,

∠ CAD = ∠ DBC = 55^{0}

(angles formed by same arc in the same segment are equal)
From the figure,

∠ DAB = ∠ CAD + ∠ BAC

∠ DAB = 55^{0} + 45^{0}

∠ DAB = 100^{0}

And,

∠ DAB + ∠ BCD = 180^{0}

(opposite angles of cyclic quadrilateral).

⟹

∠ BCD = 180^{0} - 100^{0}

⟹

∠ BCD = 80^{0}

Hence, the measure of

∠ BCD

80^{0}

.
Therefore, option 1 is correct.

In figure, $D$ is cyclic quadrilateral in which $AC$ and $BD$ are diagonals. If $∠ DBC = 55^{0}$ and $∠ BAC = 45^{0}$ , then which of the following is the measure of $∠ BCD$ ?

Solution:

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