Question

The value of $x$ in the given figure is

• A. True
• B. False
• C. ${120}^{\circ }$
• D. ${12}^{\circ }$

Answer 1

The correct option is C

${120}^{\circ }$

Sum of all the angles in a straight line $={180}^{\circ }$

$\Rightarrow (\frac{1}{3}x+8{)}^{\circ }+(\frac{3}{4}x-18{)}^{\circ }+(\frac{1}{2}x{)}^{\circ }={180}^{\circ }$

$\Rightarrow (\frac{1}{3}x+\frac{3}{4}x+\frac{1}{2}x)-18+8=180$

$\Rightarrow \left(\frac{4x+9x+6x}{12}\right)-10=180$

$\Rightarrow \left(\frac{19x}{12}\right)=190$

$\Rightarrow x=\frac{190\times 12}{19}$

$\Rightarrow x={120}^{\circ }$