(v) 22 p?q?r, 33 pq?r?
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It is given that ∠P−∠Q=42∘
It can be written as
∠P=42∘+∠Q
We know that the sum of all the angles in a triangle is 180∘.
So we can write it as
∠P+∠Q+∠R=180∘
By substituting ∠P=42∘+∠Q in the above equation
42∘+∠Q+∠Q+∠R=180∘
On further calculation
42∘+2∠Q+∠R=180∘
2∠Q+∠R=180∘−42∘
By subtraction we get
2∠Q+∠R=138∘.(i)
It is given that ∠Q−∠R=21∘
It can be written as
∠R=∠Q−21∘
By substituting the value of ∠R in equation (i)
2∠Q+∠Q−21∘=138∘
On further calculation
3∠Q−21∘=138∘
3∠Q=138∘+21∘
By addition
3∠Q=159∘
By division
∠Q=159/3
∠Q=5
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