Given: lmnp is a square a, b midpoints of lm and pn q ∈ ab m∠lpq = 45° find: m∠pqn

Since A and B are the midpoints of ML and NP, we can say that AB is parallel to MN and LP. In order to find ∠PQN, we can work with the triangles PQB and NQB. According to SAS (Side-Angle-Side) principle, these triangles are congruent. BQ is a common side for these triangles and NB=BP and the angle between those sides is 90°, i.e, ∠NBQ=∠PBQ=90°. After finding that these triangles are equal, we can say that ∠BNQ is 45°. From here, we easily find ∠PQN. It is 180 - (∠QNP + ∠NPQ) = 180 - 90 = 90°

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