Question

Question 2
Construct the Quadrilateral PLAN where
PL=4 cm, LA = 6.5 cm, $\angle P={90}^{\circ },\angle A={110}^{\circ },\angle B={85}^{\circ }$

Answer 1

Given PL=4 cm, LA = 6.5 cm, $\angle P={90}^{\circ },\angle A={110}^{\circ },\angle B={85}^{\circ }$

To construct : A quadrilateral PLAN

To find : $\angle L={360}^{\circ }-({90}^{\circ }+{85}^{\circ }+{110}^{\circ })={360}^{\circ }-{285}^{\circ }={75}^{\circ }$

Steps of construction:

(a) Draw a line segment PL=4 cm

(b) Construct angle of ${90}^{\circ }$ at P and produce the side PN.

(c) Construct angle of ${75}^{\circ }$ at L and with L as centre, draw an arc of radius 6 cm, which intersects at A.

(d) Construct $\angle A={110}^{\circ }$ at A and produce the side AN which intersects PN at N.

It is the required quadrilateral PLAN.