Question

the question is -
join q and s in the adjoining figure and prove that
angleP+angleQ + angleR+angle S equal to 360 degree​

Answer 1

Step-by-step explanation:

Given: PQRS is a quadrilateral

To Prove: Q° + P° + S° + R° = 360

Construct: Join P to R

Proof,

In ∆ QPS

We known that P° + Q1° + S1° = 180° ( Angle sum property ) [1]

Similarly, R° + Q2° + S2° = 180° [2]

Now, adding [1] & [2]

P° + Q1° + Q2° + R° + S1° + S2° = 180° + 180°

P° + Q° + R° + S° = 360°

HENCE PROVED

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