In △ACB, BC is the altitude, $∠ A = 40 ° and ∠ D = 60 °$ Find the value of x and y in the given figure.
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$x = 50^{\circ}$ and $y = 30^{\circ}$

$x = 30^{\circ}$ and $y = 40^{\circ}$

$x = 40^{\circ}$ and $y = 50^{\circ}$

$x = 30^{\circ}$ and $y = 20^{\circ}$

answer is A.

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Detailed Solution

We can find the value of x and y by using angle sum property.

The angle sum property of a triangle states that the sum of the interior angles of any triangle is always $180^{\circ}$ .

In △ACB,

$\begin{array}{l} \Rightarrow ∠ A + ∠ C + ∠ B = 180^{\circ} \\ \Rightarrow 40^{\circ} + 90^{\circ} + x = 180^{\circ} \\ \Rightarrow x = (180 - 90 - 40)^{\circ} \\ \Rightarrow x = 50^{\circ} \end{array}$

In △DCB,

$\begin{array}{l} \Rightarrow ∠ D + ∠ C + ∠ B = 180^{\circ} \\ \Rightarrow 60^{\circ} + 90^{\circ} + y = 180^{\circ} \\ \Rightarrow y = (180 - 90 - 60)^{\circ} \\ \Rightarrow y = 30^{\circ} \end{array}$