Construct a quadrilateral PQRS in which PQ=5cm, QR=6.5cm, ∠P = ∠R = 100° and ∠S = 75° .

Question

Construct a quadrilateral PQRS in which PQ=5cm, QR=6.5cm, ∠ P = ∠ R = 100 ° and ∠ S = 75 ° .

Philoid · Accepted Answer

∠Q = 360° - (∠P + ∠R + ∠S)

= 360° - (100° + 100° + 75°)

= 85°

The given quadrilateral PQRS can be drawn as follows:

Step 1: Draw a line segment PQ = 5 cm

Step 2: At P, draw an angle PQQ’ of measure 85° using protractor

Step 3: With Q as centre draw an arc on QQ’ for QR = 6.5cm.

Step 4: At S, draw an angle of measure 75° using a protractor.

Step 5: At P, draw an angle PQQ’ of measure 100° using protractor DD’ to cut at R.

Step 6: PQRS is the required quadrilateral.