In Fig. 6.45, if ST = SU, then find the values of x and y.

Formula Used/Theory:-

If 2 sides are equal then triangle is Isosceles triangle

In isosceles triangle base angles of triangles are also equal

→ Angle sum property

Sum of all angles of triangle is 180°

→ exterior angle is sum of interior opposite angles

∠TSU = 78° (Vertically opposite angles )

By isosceles triangle property

∠STU = ∠SUT

By angle sum property

∠STU + ∠SUT + ∠TUS = 180°

y + y + 78° = 180°

2y = 180° - 78° = 102° =

y = 51°

By exterior angle property

x = 78° + y

x = 78° + 51° = 129°

Result:- The value of x and y are 51° and 102°

respectively