In the diagram, △XYZ is produced to T. if |XY| = |ZY| and ∠XYT = 40°, find ∠XZT
Attached Figure / Diagram
A
110°
B
130°
C
140°
D
180°
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Isosceles Triangle. Two equal sides. Two equal angles ;
∠ X = ∠ Z
∠Y + ∠X + Z = 180 --> 40^\circ + ∠X + ∠X = 180^\circ
∠2X = 180^\circ - 40^\circ = 140^\circ
∠X = 70^\circ, i.e ∠X = 70 and ∠Z = 70^\circ.
The exterior angle of triangle is the sum of two opposite internal angles
: ∠X + ∠Y = ∠XZT
=70^\circ + 40^\circ = 110^\circ
Source: WAEC / JAMB / NECO Classroom Archive (Record #61273)