Question

Three angles of a quadrilateral are in the ratio 8 : 11 : 7. If fourth angle is 100°, then the other three angles of the quadrilateral are respectively ___.

• A. ${80}^{\circ },{120}^{\circ },{60}^{\circ }$
• B. ${80}^{\circ },{110}^{\circ },{70}^{\circ }$
• C. ${30}^{\circ },{150}^{\circ },{80}^{\circ }$
• D. ${40}^{\circ },{130}^{\circ },{90}^{\circ }$

Answer 1

The correct option is B

${80}^{\circ },{110}^{\circ },{70}^{\circ }$

Let the three angles be $8x,11xand7x$.

$\therefore 8x+11x+7x+{100}^{\circ }={360}^{\circ }\text{(Angle sum property of quadrilateral)}$

$\Rightarrow 26x+{100}^{\circ }={360}^{\circ }$

$\Rightarrow 26x={360}^{\circ }-{100}^{\circ }={260}^{\circ }$

$\Rightarrow x=\frac{{260}^{\circ }}{26}={10}^{\circ }$

$\therefore Theotheranglesare:$

$8x=8\times 10={80}^{\circ }$

$11x=11\times 10={110}^{\circ }$

$7x=7\times 10={70}^{\circ }$