In ∆PQR,if angle P-Q = 24° and angle Q-R = 21° find angle P,Q,and R.
Answers
∠P=83°,∠Q=59° and ∠R=38°
Step-by-step explanation:
It is given that ∠P−∠Q=24°
It can be written as
∠P=24°+∠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=24°+∠Q in the above equation
24°+∠Q+∠Q+∠R=180°
On further calculation
24°+2∠Q+∠R=180°
2∠Q+∠R=180°−24°
By subtraction we get
2∠Q+∠R=156°(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°=156°
On further calculation
3∠Q−21°=156°
3∠Q=156°+21°
By addition
3∠Q=177°
By division
∠Q=177÷3
∠Q=59°
By substituting ∠Q=59° in ∠P=24°+∠Q
So we get
∠P=24°+59°
By addition
∠P=83°
By substituting ∠Q in ∠Q−∠R=21∘
59°−∠R=21∘
On further calculation
∠R=59°−21°
By subtraction
∠R=38°
Therefore, ∠P=83°,∠Q=59° and ∠R=38°