Question

Find the value of x in the following figure:
​

Answer 1

First, let's understand the concept used:

→ Sum of all angles around a point is 360°

$\sf{\bigg(\dfrac{x}{2}+59^{\circ}\bigg) + \bigg(\dfrac{x}{4}\bigg) + \big(x \big) = 360^{\circ} }\\\\\\\\\implies \sf{\dfrac{x}{2}+\dfrac{x}{4}+x+ 59^{\circ} = 360^{\circ} }\\\\\\\\\implies \sf{\dfrac{x}{2}+ \dfrac{x}{4}+ x =360^{\circ} - 59^{\circ} }\\\\\\\\\implies \sf{\dfrac{2x+x+4x}{4}= 301^{\circ} }\\\\\\\\\implies \sf{\dfrac{7x}{4} = 301^{\circ} }\\\\\\\\\implies \sf{7x=301^{\circ} \times 4}\\\\\\\implies \sf{7x=1204}\\\\\\\implies \sf{x = \dfrac{1204}{7}}$

∴ x = 172°