Construct a quadrilateral PQRS where PQ = 3.5 cm, QR = 6.5 cm, ∠P = ∠R = 105° and ∠S = 75°.

We know that sum of all angles in a quadrilateral is 360⁰

+ + + = 360^o

105^o + + 75 ^o + 105 ^o = 360^o

= 360^o – 285^o = 75^o

= 75^o

Step 1: Draw the side PQ = 3.5 cm

Step 2: Draw = 105°

Step 3: Draw = 75°

Step 4: With Q as centre and radius equal to 6.5 cm draw an arc and name the point as R

Step 5: With R as centre ,construct an angle 105° and mark the point of intersection of line PX and the angle 105° as point S

Step 6: Join the points R and S

PQRS is the required quadrilateral