Question

Consider the figure:

If $\angle A={50}^{\circ }$​, $\angle B={70}^{\circ }$​, and $x=2y,$ then find the value of $x+2y.$ [3 Marks]

Answer 1

$x+y=\angle A+\angle B$
[By exterior angle property]
$={50}^o+{70}^o={120}^{\circ }$​ [1 Mark]

Also given,
$x=2y$

Thus,
$x+y={120}^{\circ }\Rightarrow 2y+y={120}^o\Rightarrow 3y={120}^o\Rightarrow y=\frac{{120}^o}{3}\Rightarrow y={40}^{\circ }$​ [1 Mark]

Hence,
$x=2y={40}^o\times 2={80}^{\circ }$​

$\therefore x+2y={80}^o+{80}^o={160}^o$

So, the value of
$x+2y={160}^{\circ }$​ [1 Mark]