10. In the adjoining figure if P: Q: R = 2: 3: 4, then find the value of P, Q, R
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Answer:
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
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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=53
∘
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