Question

If the angle of a quadrilateral are $x^o,(x-{10)}^o,(x+30{)}^o$ and $2x^o$, then the greatest angle is:

• A. ${136}^0$
• B. ${180}^0$
• C. ${68}^0$
• D. ${148}^0$

Answer 1

The correct option is A ${136}^0$

The given angles of a quadrilateral are $x^o,(x-{10)}^o,(x+30{)}^o$ and $2x^o.$

We know, that sum of four interior angles of a quadrilateral is ${360}^o$.

$\therefore$ $x+(x-10)+(x+30)+2x={360}^o$

$\Rightarrow$ $5x+{20}^o={360}^o$

$\Rightarrow$ $5x={340}^o$

$\Rightarrow$ $x=\frac{{340}^o}{5}$

$\Rightarrow$ $x={68}^o$.

Now, measure of an angles:

$x^o={68}^o$,

$(x-10{)}^o=(68-10{)}^o={58}^o$,

$(x+30{)}^o=(68+30{)}^o={98}^o$

and $2x^o=2\left({68}^o\right)={136}^o$.

$\therefore$ The greatest angle is ${136}^o$.

Hence, option $A$ is correct.