Q. 1375.0( 3 Votes )
In Fig. 6.45, if ST = SU, then find the values of x and y.
Answer :
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
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