MathematicsIf in the given figure, ΔABC is an equilateral triangle, then which of the following is the measure of ∠BDC?

If in the given figure, $ΔABC$ is an equilateral triangle, then which of the following is the measure of $∠ BDC$ ?

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A
$140^{0}$
B
$120^{0}$
C
$180^{0}$
D
$275^{0}$

Solution:

Consider the given figure,

ΔABC, ∠ A = 60^{0}

...[Equilateral triangle].
In cyclic quadrilateral

ABCD

∠ A + ∠ D = 180^{0}

....[Opposite angles of cyclic quadrilateral are supplementary]

⟹

∠ D = 180^{0} - ∠ A

⟹

∠ D = 180^{0} - 60^{0}

⟹

∠ BDC = 120^{0}

Hence, the measure of

∠ BDC

120^{0}

.
Therefore, option 2 is correct.

If in the given figure, $ΔABC$ is an equilateral triangle, then which of the following is the measure of $∠ BDC$ ?

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