Question

Consider the figure:

If BC = AC, x = 2y, and angle ∠ACB = 60^o. Then find the value of ∠B + y (in degrees).

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Answer 1

$\angle$C = ${60}^{\circ }$​, and BC = AC,
By angle sum property of triangle, $\angle$A = $\angle$B = ${60}^{\circ }$​.
$\angle$A + $\angle$B + x + y = ${60}^{\circ }$ + ${60}^{\circ }$ + ${120}^{\circ }$​ = ${240}^{\circ }$​
$\Rightarrow$ y + 2y = ${120}^{\circ }$
$\Rightarrow$ y = ${40}^{\circ }$.
​Hence $\angle$B + y = ${100}^{\circ }$​.