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Sum of Measures of Exterior Angles of a Polygon

In the given ...

Question

In the given figure $A B C$ is a triangle in which $A B = A C$ . $X$ and $Y$ are the Exterior angles formed by producing $A B$ and $A C$ show that $X = Y$ .

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Solution

$A B = A C$
That means $∠ B = ∠ C$
$∠ B = X$ (vertically opposite angles)
$∠ C = Y$ (vertically opposite angles)
$X + Y$ .

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