In the figure given alongside, find the values of $x$ and $y .$

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Solution

We know that the exterior angle of a triangle is equal to the sum of the interior opposite angles.
$∴ ∠ B A C + ∠ A B C = ∠ A C D$
$\Rightarrow x + 68^{\circ} = 130^{\circ}$
$\Rightarrow x = 62^{\circ}$
The Sum of all the angles in a triangle is $180^{\circ}$
$∴ ∠ B A C + ∠ A B C + ∠ A C B = 180^{\circ}$
$\Rightarrow 62^{\circ} + 68^{\circ} + y = 180^{\circ}$
$\Rightarrow y = 50^{\circ}$

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In the figure given alongside, find the values of x and y.

We know that the exterior angle of a triangle is equal to the sum of the interior opposite angles.∴∠BAC+∠ABC=∠ACD⇒x+68∘=130∘⇒x=62∘The Sum of all the angles in a triangle is 180∘∴∠BAC+∠ABC+∠ACB=180∘⇒62∘+68∘+y=180∘⇒y=50∘

In the figure given alongside, find the values of $x$ and $y .$