Question

The angle of a triangle are $(x-40{)}^o,(x-20{)}^{o}and{(\frac{1}{2}x-10)}^o$. Find the value of x.

• A. $10$
• B. $50$
• C. $90$
• D. $100$

Answer 1

The correct option is D $100$

The angles of a triangle are ${(x-40)}^{\circ },(x-{20}^{\circ }),{(\frac{x}{2}-10)}^{\circ }$

The sum of the measures of the interior angles of a triangle is ${180}^{\circ }$

So,

$x-40+x-20+\frac{x}{2}-10=180$

$\frac{5x}{2}-70=180$

$\frac{5x}{2}=180+70=250$

$x=\frac{250\times 2}{5}=100$