Question

Construct a quadrilateral $ABCD$ when $BC=5.5cm,CD=4.1cm,\angle A={70}^{\circ },\angle B={110}^{\circ }$ and $\angle D={85}^{\circ }$

Answer 1

Given $\angle A={70}^{\circ },\angle B={110}^{\circ },\angle D={85}^{\circ }$
But $\angle A+\angle B+\angle C+\angle D={360}^{\circ }$
(Sum of angles of a quadrilateral)
$\Rightarrow {70}^{\circ }+{110}^{\circ }+\angle C+{85}^{\circ }={360}^{\circ }$
$\Rightarrow {265}^{\circ }+\angle C={360}^{\circ }$
$\Rightarrow \angle C={360}^{\circ }-{265}^{\circ }={95}^{\circ }$
steps of construction :
(i) Draw a line segment $BC=5.5cm$.
(ii) At $B$, using protractor draw a ray $BX$ making an angle of ${110}^{\circ }$
(iii) At $C$, draw another ray $CY$ making an angle of ${95}^{\circ }$ and cut off $CD=4.1cm$.
(iv) At $D$, draw a ray $DZ$ making an angle of ${85}^{\circ }$ which intersects $BX$ at $A$.

Then $ABCD$ is the required quadrilateral.