Question

Can someone help i have been stuck

Answer 1

b = 17

Explanation:

Step 1:

Given PQ = QR in triangle PQR.

So, triangle PQR is an isosceles triangle.

Hence,
`\angle \mathrm{QPR}=\angle \mathrm{QRP}=47^(\circ)` – – – – (1)

Step 2:

Let us consider two triangles PQS and SQR.

`\angle \mathrm{PQS}=\angle \mathrm{SQR}=\mathrm{a}` (given angle)

PQ = QR (given side)

`\angle \mathrm{QPS}=\angle \mathrm{QRS}=47^(\circ)` (angle proved in equation (1))

`\therefore \Delta PQS=\Delta SQR` (by ASA congruence criterion)

Hence by corresponding parts of congruence triangles,

⇒ PS = SR

⇒ PS = 17

⇒ b = 17

Hence the value of b is 17.