#### Question

Angles Q and R of a ΔPQR are 25° and 65°.

Write which of the following is true:

(1) PQ^{2} + QR^{2}= RP^{2}

(2) PQ^{2} + RP^{2}= QR^{2}

(3) RP^{2} + QR^{2}= PQ^{2}

^{}

#### Solution

The sum of the measures of all interior angles of a triangle is 180º.

∠PQR + ∠PRQ + ∠QPR = 180º

25º + 65º + ∠QPR = 180º

90º + ∠QPR = 180º

∠QPR = 180º − 90º = 90º

Therefore, Δ PQR is right-angled at point P.

Hence, (PR)^{2} + (PQ)^{2} = (QR)^{2}

Thus, (ii) is true.

Is there an error in this question or solution?

Solution Angles Q and R of a δPqr Are 25° and 65°. Write Which of the Following is True: Concept: Sum of the Lengths of Two Sides of a Triangle.