Question

show your working for the given figure

Find the measures of the unknown angles using the angle sum property.

∠PRQ=∠PQR=∠RPQ

Answer 1

Answer:

∠PRS=60°

∠PSR=102°

∠PSQ=98°

∠SPQ=42°

∠SQP=60°

Step-by-step explanation:

In triangle PQR, let angle PRQ, angle PQR and angle RPQ=x°

x+x+x=180                (angle sum property of triangle)

3x=180

x=60°

Therefore, angle PRQ, angle PQR and angle RPQ=60°

Now, for angle QPS we have

∠RPQ=∠SPQ + ∠SPR

60= ∠SPQ + 18

∠SPQ=42°

Now, for angle PSR,

PSR + SPR + PRS=180  (angle sum property)

PSR + 18 + 60=180

PSR=102°

for angle PSQ you can use the same method as above of angle sum property in triangle and find that the angle PSQ=98°

Pretty boring to type but there you go....