MathematicsIn figure, ABCD is a cyclic quadrilateral. If ∠D=1200, then which of the following is the measure of ∠CBE?

In figure, $ABCD$ is a cyclic quadrilateral. If $∠ D = 120^{0}$ , then which of the following is the measure of $∠ CBE$ ?

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A
$120^{0}$
B
$60^{0}$
C
$180^{0}$
D
$90^{0}$

Solution:

Consider the given figure,

From the figure-

ABCD

is a cyclic quadrilateral.

∠ D = 120^{0}

.
Sum of opposite angles of cyclic quadrilateral are supplementary.
Then,

∠ ADC + ∠ ABC = 180^{o}

⟹

120^{o} + ∠ ABC = 180^{o}

⟹

∠ ABC = 180^{o} - 120^{o}

⟹

∠ ABC = 60^{o}

Also,

∠ ABC + ∠ CBE = 180^{o}

...(Linear pair)

⟹

∠ 60^{o} + ∠ CBE = 180^{o}

⟹

∠ CBE = 180^{o} - 60^{o}

⟹

∠ CBE = 120^{o}

Hence, the measure of

∠ CBE

120^{o}

.
Therefore, option 1 is correct.

In figure, $ABCD$ is a cyclic quadrilateral. If $∠ D = 120^{0}$ , then which of the following is the measure of $∠ CBE$ ?

Solution:

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