Question

in triangle PQR PQ = QR. A is a point on PQ and B is a point on PR, so that QR=RA=AB=BP. (i)Show that angle A:angle B=1:3 (ii) find the value of angle Q​

Answer 1

Answer:

In triangle PAB

AB=PB

So angle PAB=angle P

angle ABR=PAB+P

In triangle ABR

AB=AB

so, ABR=ARB=2P

BAR=180- 4 angle P

Sum of linear pair angle is 180

In triangle QAR =3 Angle P

Angle QAR =3P

In triangle PQR

PQ = PR

Angle Q =Angle R

Angle P+ Angle R +Angle Q=180

1/3 Angle Q +AngleQ+AngleQ=180

Angle Q = 77.14