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The angles of a quadrilateral are in A.P. with a common difference of 10 degrees. Find the smallest angle.

  • A.65°
  • B.75°
  • C.85°
  • D.90°

Answer: B

Let the angles be \(a, a+10, a+20, a+30\). The sum of angles in a quadrilateral is 360°. So, \(a + (a+10) + (a+20) + (a+30) = 360 \Rightarrow 4a + 60 = 360 \Rightarrow 4a = 300 \Rightarrow a = 75\). The smallest angle is 75°.

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