Question

In XYZW, l(XY) = 5.5 cm, l(XW) = 3 cm, m∠X = 70°, m∠Y = 95° and m∠Z = 85°.

Answer 1

Given: l(XY)=5.5 cm, l(XW)=3 cm, m$\angle$X=70°, m$\angle$Y=95° and m$\angle$Z=85°.
First, draw a rough sketch of quadrilateral XYZW and indicate the given lengths, as shown below.
The angle formed at W will be required in the construction. This angle can be calculated based on the fact that sum of all the angles of a quadrilateral is 360°. So, m$\angle$W=360° − 250°=110°

Steps of Construction:
(1) Draw a line segment XY = 5.5 cm.

(2) Then, construct an angle of 70° at X. Mark the point W, such that WX = 3 cm.

(3) Now, construct an angle of 110° at W and an angle of 95° at Y to meet the two line segments at Z.

Thus, XYZW is the required quadrilateral.