In the diagram, △XYZ is produced to T. if |XY| = |ZY| and ∠XYT = 40°, find ∠XZT

Explanation

Isosceles Triangle. Two equal sides. Two equal angles ;

∠ X = ∠ Z

∠Y + ∠X + Z = 180  --> 40° + ∠X + ∠X = 180°

∠2X = 180° - 40° = 140°

∠X = 70°, i.e ∠X = 70 and ∠Z = 70°.

The exterior angle of triangle is the sum of two opposite internal angles

: ∠X + ∠Y = ∠XZT

=70° + 40° = 110°