Question

oly WILTU B В NIE х 3 А Fig. 5​

Answer 1

$\large\bf\underline\red{Answer \: :-}$

Given :

• $\sf{ \angle AOB = \frac{x}{2} }$
• $\sf{ \angle BOC = \frac{x}{3} }$

To find :

• x

Rule : Supplementary angles are 180°

Hence, $\sf{ \frac{x}{2} + \frac{x}{3} = 180 \degree}$

Finding x

$\sf\longmapsto{ \frac{x}{2} + \frac{x}{3} = 180 \degree} \: \: \: \: \\ \\ \sf\longmapsto{ \frac{3x + 2x}{6} = 180 \degree} \\ \\ \sf\longmapsto{ \frac{5x}{6} = 180 \degree } \: \: \: \: \: \: \: \: \: \\ \\ \sf\longmapsto{5x = 180 \degree \times 6} \: \: \\ \\ \sf\longmapsto{5x = 1080} \: \: \: \: \: \: \: \: \: \: \\ \\ \sf\longmapsto{x = \frac{1080}{5} } \: \: \: \: \: \: \: \: \: \: \\ \\ \bf\longmapsto{ \boxed{ \bf\red{x =216 \degree }}} \: \: \: \: \: \: \:$

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Verification :

Put x = 216°

$\sf\longmapsto{ \frac{x}{2} + \frac{x}{3} = 180 \degree} \: \: \: \: \: \: \: \: \: \: \\ \\ \sf\longmapsto{ \frac{216}{2} + \frac{216}{3} = 180 \degree} \\ \\ \sf\longmapsto{108 + 72 = 180 \degree} \: \: \: \: \: \\ \\ \bf\longmapsto \red{180 \degree = 180 \degree} \: \: \: \: \: \: \: \:$

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