Question

Three angles of a quadrilateral are in the ratio 8 : 2 : 3. If fourth angle is 100°, then the other three angles of the quadrilateral are respectively ___.

• A. ${140}^{\circ },{60}^{\circ },{60}^{\circ }$
• B. ${80}^{\circ },{110}^{\circ },{70}^{\circ }$
• C. ${80}^{\circ },{120}^{\circ },{60}^{\circ }$
• D. ${30}^{\circ },{150}^{\circ },{80}^{\circ }$

Answer 1

The correct option is A ${140}^{\circ },{60}^{\circ },{60}^{\circ }$

Let the three angles be $8x,2xand3x$.

$\therefore 8x+2x+3x+{100}^{\circ }={360}^{\circ }\text{(Angle sum property of quadrilateral)}$

$\Rightarrow 13x+{100}^{\circ }={360}^{\circ }$

$\Rightarrow 13x={360}^{\circ }-{100}^{\circ }={260}^{\circ }$

$\Rightarrow x=\frac{{260}^{\circ }}{13}={20}^{\circ }$

$\therefore Theotheranglesare:$

$8x=8\times {20}^{\circ }={160}^{\circ }$

$2x=2\times {20}^{\circ }={40}^{\circ }$

$3x=3\times {20}^{\circ }={60}^{\circ }$