Question

Consider the figure:

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

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Answer 1

$\angle$C = ${60}^{\circ }$​ and BC = AC,
By angle sum property of triangle, $\angle$A = $\angle$B = ${60}^{\circ }$​

Also,
$\angle ACB+\angle x+\angle y={180}^0$ [ BCD is straight line]
$⟹{60}^{\circ }+2y+y={180}^{\circ }$​
$⟹{60}^{\circ }+3y={180}^{\circ }$
$⟹3y={180}^{\circ }-{60}^{\circ }$​
$⟹y={40}^{\circ }$

Hence, $\angle B+y={60}^{\circ }+{40}^{\circ }={100}^{\circ }$​