The sum of the four angles of a quadrilateral is $360 °$
In a quadrilateral $A B C D, ∠ A + ∠ C = 180 °,$ then $∠ B + ∠ D =$

$360 °$

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$180 °$

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$80 °$

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$100 °$

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Solution

The correct option is B
$180 °$

Choose the correct option.
By the angle sum property of the quadrilateral.
$∠ A + ∠ B + ∠ C + ∠ D = 360 °$
we know that the $∠ A + ∠ C = 180 °$
$\begin{array}{rcl} ∠ B + ∠ D & = & 360 ° - 180 ° \\ = & 180 ° \end{array}$
Hence, the $∠ B + ∠ C$ is $180 ° .$
Hence, the correct option is B.

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