Question

In ∆PQR, ∠P – ∠Q = 28° and ∠R – ∠Q = 2°. Find all the angles of the triangle. ( I need step by step explanation)

Answer 1

Answer:

50, 78 , 52

Step-by-step explanation:

Sum of angles of a triangle equal to $180^{o}$

∠P+ ∠Q+ ∠R= $180^{o}$  ----- ( 1 )

here ∠P- ∠Q=$28^{o}$   i.e,   ∠P=$28^{o}$ +∠Q  ---- ( 2 )

similarly,

∠R-∠Q= $2^{o}$   i.e,  ∠R= $2^{o}$ +∠Q   ------------ ( 3 )

Put these values in equation ( 1 )

$28^{o}$ +∠Q +∠Q + $2^{o}$ +∠Q =$180^{o}$

3∠Q+$30^{o}$ = $180^{o}$

3∠Q= $180^{o}$ - $30^{o}$

3∠Q= $150^{o}$

∠Q= $\frac{150}{3}$

∠Q= $50^{o}$

Using Equation ( 2 )

∠P=$28^{o}$ +$50^{o}$ = $78^{o}$

Using Equation ( 3 )

∠R= $2^{o}$ +$50^{o}$ = $52^{o}$