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  2. Construct the following quadrilaterals. (ii) Quadrilateral PLAN PL = 4 cm LA = 6.5 cm ∠P = 90° ∠A = 110° ∠N = 85°
# NCERT

Q1. Construct the following quadrilaterals.

(ii) Quadrilateral PLAN
PL = 4 cm
LA = 6.5 cm
∠P = 90°
∠A = 110°
∠N = 85°

Answers (1)
H Harsh Kankaria

Given, PLAN is a quadrilateral.

PL = 4 cm
LA = 6.5 cm
∠P = 90°
∠A = 110°
∠N = 85°

We know, Sum of all angles of a quadrilateral = 360°

\therefore ∠P + ∠L + ∠A+ ∠N = 360° \implies  90° + ∠L + 110° + 85° = 360°

\implies ∠L = 360° - 285° = 75°

Steps of Construction

Step 1. Draw a line segment PL = 4 cm. Construct an angle of 75° at L. As LA =6.5 cm, draw an arc with L as centre and radius = 6.5 cm. We get point A.

Step 2. Construct an angle of 110° at A.

Step 3. Construct an angle of  90° at P. This ray intersects the previous one at N. 

PLAN is the required quadrilateral.

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