Question

In a quadrilateral PQRS,angle's P + S =150 ,angle's P:S=3:2 and angle's Q:R=3:4. Find the angle's PQR and S

Answer 1

P+S=150

P:S=3:2

p = 150x3/5=90

S = 150x2/5=60

Total angle of Quadrilateral = 360

Q+R=360-150 =210

Q: R=3:4

Q=210x3/7=90

R = 210x4/7=120

P=90,Q=90, R = 120, S=60

Answer 2

PQRS is a quadrilateral,  ( given)

∠P+ ∠S =150   ( given )

∠P: ∠S =3:2  ( given)

∴∠P = 150 × $\frac{3}{5}$ =90

∠S = 150x $\frac{2}{5}$ =60

We know that sum of four angles of a Quadrilateral = 360

∠Q + ∠R=360-150 =210

∠Q:∠ R=3:4  ( given)

∠Q=210 x $\frac{3}{7}$ =90

∠R = 210x $\frac{4}{7}$ =120

∴ ∠P=90,

∠Q=90,

∠ R = 120,

∠ S=60

Ans :- Angles of  quadrilateral PQRS are  ∠P=90, ∠Q=90, ∠ R = 120,∠ S=60