#### Question

Construct a quadrilateral ABCD, where ∠A = 65°, ∠B = 105°, ∠C = 75° BC = 5.7 cm and CD = 6.8 cm.

#### Solution

\[\text { We know that the sum of all the angles in a quadrilateral is 360 } . \]

\[\text { i . e} . , \angle A + \angle B + \angle C + \angle D = 360^\circ\]

\[ \Rightarrow \angle D = 115^\circ\]

Steps of Construction:

Step I: Draw BC = 5 . 7 cm .

\[\text { Step II: Construct } \angle XBC = 105^\circ\text { at B and } \angle BCY = 105^\circ at C . \]

Step III : With C as the centre and radius 6 . 8 cm, cut off CD = 6 . 8 cm .

\[\text { Step IV: At D, draw } \angle CDZ = 115^\circ \text { such that it meets BY at A } . \]

The quadrilateral so obtained is the required quadrilateral .

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Solution Construct a Quadrilateral Abcd, Where ∠A = 65°, ∠B = 105°, ∠C = 75° Bc = 5.7 Cm and Cd = 6.8 Cm. Concept: Constructing a Quadrilateral - When Two Adjacent Sides and Three Angles Are Known.