Math, asked by kakansha760, 6 months ago

Find ∠Q if in PQR, ∠P - ∠Q= 42 ˚ and ∠Q - ∠R= 21 ˚.​

Answers

Answered by saxenalavi422
2

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

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

.

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