The angles of a quadrilateral are in AP whose common difference is 10. Find the smallest angle of the quadrilateral.


Answer:

75

Step by Step Explanation:
  1. The angles of the quadrilateral are in AP with the common difference of 10.

    Let the angles be x,x+10,x+20, and x+30.
  2. We know that the sum of all angles of a quadrilateral is 360. Thus x+x+10+x+20+x+30=3604x+60=3604x=360604x=300x=3004x=75
  3. Let us now substitute the value of x to get the four angles. x=75x+10=75+10=85x+20=75+20=95x+30=75+30=105
  4. Hence, the smallest angle of the quadrilateral is 75 .

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