In the diagram, △XYZ is produced to T. if |XY...
In the diagram, △XYZ is produced to T. if |XY| = |ZY| and ∠XYT = 40°, find ∠XZT
A.
110°
B.
130°
C.
140°
D.
180°
Correct answer is A
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°