Question

Question 140

In the given figure, if y is five times x, find the value of z.

Answer 1

Given, $y=5x$
According to the angle sum property of a triangle,
${60}^{\circ }+x+y={180}^{\circ }$
$\Rightarrow {60}^{\circ }+x+5x={180}^{\circ }$ $[\because y=5x]$
$\Rightarrow {60}^{\circ }+6x={180}^{\circ }\Rightarrow 6x={180}^{\circ }-{60}^{\circ }={120}^{\circ }\Rightarrow x=\frac{{120}^{\circ }}{6}={20}^{\circ }\therefore y=5x=5\times 20={100}^{\circ }$
According to the exterior angle property,
$z={60}^{\circ }+y$
$={60}^{\circ }+{100}^{\circ }$ $[\because y={100}^{\circ }]$
$={160}^{\circ }$