# Angles Q and R of a ∆PQR are 25º and 65º. Write which of the following is true:

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

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

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

**Solution:**

In this question it is clear from the figure two angles of a triangle are given and we must find out the third angle by using the angle sum property that is the sum of three interior angles of a triangle is 180°.

By using this property, we got the value of the third angle that is P = 90° that means the side opposite to P is hypotenuse that is QR.

As one of the angles is 90° that means it is a right-angled triangle and the square of the hypotenuse is equal to the sum of the square of the other two sides.

We know that, sum of interior angles of a triangle is 180°.

∠P + ∠Q + ∠R = 180°

∠P + 25° + 65° + 180°

∠P + 90° + 180°

∠P + 180° + 90°

∠P + 90°

Thus, triangle PQR is a right angled at P

Therefore, by Pythagoras theorem

(P)^{2} + (B)^{2 }= (H )^{2}

(QP)^{2 }+ (PR)^{2} = (QR)^{2}

Hence, option (ii) is correct.

Useful Tip:

Whenever you encounter a problem of this kind, it is best to think of the Pythagoras property if one of the three angles is 90°then the square of the hypotenuse or greater side is equal to the sum of the square of the other two sides.

**Video Solution:**

## Angles Q and R of a ∆PQR are 25º and 65º. Write which of the following is true: (i)PQ^{2} + QR^{2} = RP^{2 }(ii)PQ^{2 }+ RP^{2 }= QR^{2 }(iii)RP^{2} + QR^{2} = PQ^{2}

### NCERT Solutions for Class 7 Maths - Chapter 6 Exercise 6.5 Question 6

Angles Q and R of a ∆PQR are 25º and 65º. Write which of the following is true:(i)PQ^{2} + QR^{2} = RP^{2 }(ii)PQ^{2 }+ RP^{2 }= QR^{2 }(iii)RP^{2} + QR^{2} = PQ^{2}

(QP)^{2} + (PR)^{2} = (QR)^{2} Hence, option (ii) is correct