In $△ A B C$ , $A B = A C$ and $∠ A : ∠ B = 8 : 5$ . Then measure of $∠ A$ in degrees is

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Solution

$∠ A : ∠ B = 8 : 5$
Let $∠ A = 8 x, ∠ B = 5 x$
Given, $A B = A C$
Thus, $∠ B = ∠ C = 5 x$ (Isosceles triangle property)
Sum of angles of triangle = 180
$8 x + 5 x + 5 x = 180$
$18 x = 180$
$x = 10^{\circ}$
hence, $∠ A = 8 x = 80^{\circ}$

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