Question

P, Q & R form a right-angled triangle.
R, S & P lie on a straight line.
PS = SQ and
∠
SQR = 40°.
Work out
∠
RPQ, explaining each stage of your working in the comment box.

The diagram is not drawn accurately.

Answer 1

Given :

• ∠SQR = 40°.

To Find :

• ∠RPQ

Solution :

In ∆ PQR

→ ∠RPQ + ∠RQP + ∠PRQ = 180°

→ ∠RPQ + (∠RQS + ∠PQS) + ∠PRQ = 180°

→ ∠RPQ + (40° + ∠PQS) + 90° = 180°

→ ∠RPQ + ∠PQS + 40° + 90° = 180°

→ 2∠RPQ + 130° = 180° [ ∠RPQ and ∠PQS are base angles of an isosceles triangle ]

→ 2∠RPQ = 50°

→ ∠RPQ = 50/2

→ ∠RPQ = 25°

Hence,

• ∠RPQ = 25°.

Answer 2

Answer:

16

Step-by-step explanation: