Question

Three angles of a quadrilateral are in the ratio 4 : 6 : 3. If fourth angle is 100°, find the other three angles of the quadrilateral.

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

Answer 1

The correct option is A

${80}^{\circ },{120}^{\circ },{60}^{\circ }$

Let the three angles be $4x^{\circ },6x^{\circ }and3x^{\circ }$.

$\therefore 4x+6x+3x+{100}^{\circ }={360}^{\circ }$ (Angle sum property of quadrilateral)

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

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

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

The other angles are -

$4x=4\times {20}^{\circ }={80}^{\circ }$

$6x=6\times {20}^{\circ }={120}^{\circ }$

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