Question

construct a quadrilateral PQRS where PQ = 5.4 cm, angle P is 60°, angle Q is 105°, angle R is 75°, angle S is 120°​

Answer 1

Answer:

Given : a quadrilateral PQRS where PQ = 5.4 cm, ∠P = 60°. ∠Q = 105°, ∠R = 75° and ∠S = 120°.

To find : Construct Quadrilateral

Solution:

∠P + ∠S = 180° ∠Q + ∠R = 180°

=> PQ ║ RS

PQ = 5.4 cm

we need one more information length of Either QR , RS or PS

Step 1 : Draw a line segment PQ = 5.4 cm

Step 2 : Draw an angle of 60° at P Using protractor

Step 3 : Draw an angle of 105° at Q using protractor

Step 4 : Draw a line parallel to PQ intersecting angles drawn at R ( 105° & S (60°)

You can draw as many quadrilaterals as you want positioning RS

so we need either of length QR , RS or PS to have unique quadrilateral

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Step-by-step explanation:

steps for construction :-

1) draw line segment pq = 5.4 cm

2) draw an angle of 60 degree at point p to x and 105 degree at pont Q ti Y.

3) now from point p cuts an arc of any length at px at point S.

4) draw an angle of 120 degree at S, which meets QY at R

thus, PQRS is a required quadrilateral

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