Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q1

LMNO is a square. PQN and PLQ are isosceles triangles. Angle QNM is 23 degrees. Find Angle NPQ.

Solution

Angle PNO --> 23 deg (mirror image of Angle MNQ)

Angle OPN --> 90 deg - 23 deg = 67 deg

Angle LPQ --> 45 deg (Triangle LQP is isosceles and Angle LPQ is a rt angle)

Angle NPQ --> (180 - 45 - 67) deg = 68 deg

Answer: 68 degrees

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