Question

The angles of a triangle are$(2x+{30}^o),(3x-{110}^o)$ and $(\frac{5}{2}x+{20}^o)$, find the value of $x$.

• A. ${16}^o$
• B. ${32}^o$
• C. ${40}^o$
• D. ${50}^o$

Answer 1

The correct option is B ${32}^o$

Angle sum property of triangle:

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

The three angles given are $(2x+{30}^{\circ })$, $(3x-{110}^{\circ })$ and $(\frac{5}{2}x+{20}^{\circ })$

So,

$2x+{30}^{\circ }+3x-{110}^{\circ }+\frac{5}{2}x+{20}^{\circ }={180}^{\circ }$

$\frac{15}{2}x-{60}^{\circ }={180}^{\circ }$

$\frac{15}{2}x={240}^{\circ }$

it implies,

$x=\frac{{480}^{\circ }}{15}={32}^{\circ }$