Q3 of 158 Page 159

In Fig. 6.7, PQ = PS. The value of x is

Given: In ΔPQS

PQ = PS, Exterior angle with Q is 110°

In ΔPSR

∠PRS = 25°, ∠RPS = x

Formula Used/Theory:-

Exterior angle of triangle is equal to sum of 2 opposite interior angles .

As RQ is straight line

∠PQS + 110° = 180°

∠PQS = 180° - 110°

∠PQS = 70°

As ΔPQS is isosceles triangle and PQ = PS

∴ ∠PQS = ∠PSQ

⇒ ∠PSQ = 70°

In ΔPSR

With exterior angle ∠PSQ equal to sum of opposite interior angles

∠PSQ = ∠SPR + ∠PRS

70° = x + 25°

x = 70° - 25°

x = 45°

The sides of a triangle have lengths (in cm) 10, 6.5 and a, where a is a whole number. The minimum value that a can take is

Triangle DEF of Fig. 6.6 is a right triangle with ∠E = 90°.

What type of angles are ∠D and ∠F?

In a right-angled triangle, the angles other than the right angle are

In an isosceles triangle, one angle is 70°. The other two angles are of

(i) 55° and 55°

(ii) 70° and 40°

(iii) any measure

In the given option(s) which of the above statement(s) are true?