Question

Find, correct to the nearest degree, the three angles of the triangle with the given vertices. p(1, 0), q(0, 1), r(4, 4)

Answer 1

A geometry app shows the angles to be
  ∠p ≈ 82°
  ∠q ≈ 82°
  ∠r ≈ 16°

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The length of pq is √2, and the length of pr is 5. Then
  cos(p) = √2/(2·5)
  p = arccos(√2/10) = 81.87°
The triangle is isosceles, so q = 81.87° and r = 180° -2*81.87° = 16.26°.