Construct a quadrilateral ABCD in which AB=5.6cm, BC=4cm, ∠A= 50°, ∠B = 105° and ∠D = 80°.

Question

Construct a quadrilateral ABCD in which AB=5.6cm, BC=4cm, ∠ A = 50 ° , ∠ B = 105 ° and ∠ D = 80 ° .

Philoid · Accepted Answer

∠C = 360° - (∠A + ∠B + ∠D)

= 360° - (50° + 105° + 80°)

= 125°

The given quadrilateral ABCD can be drawn as follows:

Step 1: Draw a line segment AB = 5.6 cm

Step 2: At B, draw an angle BCC’ of measure 125° using protractor

Step 3: With C as centre draw an arc on CC’ for BC = 4cm.

Step 4: At D, draw an angle of measure 80° using a protractor.

Step 5: At B, draw an angle BCC’ of measure 105° using protractor DD’ to cut at A.

Step 6: ABCD is the required quadrilateral.