Question

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

• A. ${60}^{\circ }$
• B. ${75}^{\circ }$
• C. ${100}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is C ${100}^{\circ }$

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

We know that sum of all the angles of a triangle $={180}^{\circ }$
$(x-40{)}^{\circ }+(x-20{)}^{\circ }+(\frac{x}{2}-10{)}^{\circ }={180}^{\circ }$
$\Rightarrow x+x+\left(\frac{x}{2}\right)–{40}^{\circ }–{20}^{\circ }–{10}^{\circ }={180}^{\circ }$
$\Rightarrow x+x+\left(\frac{x}{2}\right)–{70}^{\circ }={180}^{\circ }$
$\Rightarrow \left(\frac{5x}{2}\right)={180}^{\circ }+{70}^{\circ }$
$\Rightarrow \left(\frac{5x}{2}\right)={250}^{\circ }$
$\Rightarrow x=\left(\frac{2}{5}\right)\times {250}^{\circ }$
$\Rightarrow x={100}^{\circ }$
Hence, the value of $x$ is ${100}^{\circ }.$