In angle PQR,if angle p- angle q=42 and angle q - angle r =21 ,find angle p,angle q and angle r
Answers
Answer:It is given that ∠P−∠Q=42
It can be written as
∠P=42
∘
+∠Q
Step-by-step explanation: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=53
∘
By substituting ∠Q=53
∘
in ∠P=42
∘
+∠Q
So we get
∠P=42
+53
By addition
∠P=95
By substituting ∠Q in ∠Q−∠R=21
53
−∠R=21
On further calculation
∠R=53
−21
By subtraction
∠R=32
Therefore, ∠P=95
∘
,∠Q=53
and ∠R=32