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Given square ABCD. Two isosceles triangles ABP and BCQ are constructed with bases AB and BC . Each of these triangles has vertex angle of 80°. Point P lies in the interior of the square, while point Q lies outside of the square. Find the angle measure between PQ and BC

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Answer:

  85°

Step-by-step explanation:

Each of the isosceles triangles PAB and QBC has interior base angles of ...

  (180° -80°)/2 = 50°

Then angle PBC is 90° -50° = 40°.

Segments PB and QB are the same length, so triangle PBQ is an isosceles right triangle. This means angle BPQ is 45°. Angle QEB is the sum of the remote interior angles of ∆BEP, so is 45° +40° = 85°.

The acute angle between PQ and BC is 85°.

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