Question

If the degree measures of the angles of quadrilateral are 4x, 7x, 9x and 10x, what is the sum of the measures of the smallest angle and largest angle ?

• A. ${140}^{\circ }$
• B. ${150}^{\circ }$
• C. ${168}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

The correct option is C

${168}^{\circ }$

Sum of the angles of a quadrilateral = ${360}^{\circ }$

$\therefore 4x+7x+9x+10x={360}^{\circ }$

$\Rightarrow 30x={360}^{\circ }$

$\Rightarrow x=\frac{{360}^{\circ }}{30}={12}^{\circ }$

Now sum of smallest and largest angle

=$4\times {12}^{\circ }+10\times {12}^{\circ }$

= ${48}^{\circ }+{120}^{\circ }={168}^{\circ }$