In PQR p=2 Q and 2r=3 Q, calculate the angles of PQR.
Answers
Alright, this is a simple algebraic problem.
Given:
p = 2q
2r = 3q => r = 3q/2
So, as we know, by angle sum property, p + q + r = 180*
So,
2q + q + 3q/2 = 180*
4q/2 + 2q/2 + 3q/2 = 180
(4q + 2q + 3q)/2 = 180
9q/2 = 180
9q = 180*2
9q = 360
q = 360/9
q = 40
Now, knowing this value we can find the remaining values
p = 2q = 2*40 = 80*
q = 40*
r = 3q/2 = 3*40/2 = 120/2 = 60*
So, the three angles of PQR are p = 80*, q = 40* and r = 60*
Hope this Helped!
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Answer:
∠P = 80, ∠Q = 40, ∠R = 60
Step-by-step explanation:
In ΔPQR, ∠P = 2 *∠Q and, 2 *∠R = 3 *∠Q
We know that sum of three angles is 180 degree that is ∠P + ∠Q + ∠R = 180
∠Q = ∠P/2 -------(1)
And, ∠R = 3 *∠Q /2
or, ∠R = 3 *∠P/4 ------(2)
Then, from the values of (1) and (2), ∠P + ∠P/2 + 3 *∠P/4 = 180
Or, ∠P * (1 + 1/2 + 3/4) = 180
Or, ∠P = 80
From (1), ∠Q = 40 and from (2) ∠R = 60.