Answer:
Δ MNQ ≅ Δ POQ ( BY Angle Angle Side)
Step-by-step explanation:
Given:
m∠NQM = 40°
m∠NQO = 100°
MNOP is a Rectangle
So we can say that:
Property of rectangle:
All angles of rectangle are 90°
Opposite sides of Rectangle are equal and parallel to each other
MN ≅ PO (opposite side of rectangle)
∠NMQ ≅ ∠OPQ (Both angles are 90°)
Now By Straight Angle property
m∠NQM + m∠NQO + m∠OQP = 180° (angles of straight line)
Substituting the values we get;
40° + 100° + m∠OQP = 180°
140° + m∠OQP = 180°
m∠OQP = 180° - 140° = 40°
So m∠OQP = m∠NQM = 40°
m∠OQP ≅ m∠NQM (Equals angles are congruent to each other)
Hence In Δ MNQ and Δ POQ
m∠OQP ≅ m∠NQM
∠NMQ ≅ ∠OPQ (Both angles are 90°)
MN ≅ PO (opposite side of rectangle)
Δ MNQ ≅ Δ POQ ( BY Angle Angle Side)
Hence Proved...
