Question

Consider the figure:

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

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Answer 1

$\angle$ACB = ${60}^{\circ }$​ and BC = AC,
$\angle$A = $\angle$B [Angle opposite to equal sides are also equal]
By angle sum property of triangle, $\angle$A = $\angle$B = ${60}^{\circ }$​
x + y = $\angle$A + $\angle$B = ${120}^{\circ }$ [Exterior angle property]

$\angle$A +$\angle$B +$\angle$x +$\angle$y = ${60}^{\circ }$ ​+${60}^{\circ }$ ​+${120}^{\circ }$​ = ${240}^{\circ }$​​​​​​​​