Question

6) The interior angles of a quadrilateral are in an A.P. The smallest angle is 15°. Find the
remaining angles.
​

Answer 1

Answer:

The 4 angles add to 360, so if one is 15, then the other 3 add to 345. The average is then 115 degrees. So if they are in AP (=arithmetic progression) then the three angles are 115+d, 115, and 115-d, and the 4th “smallest” angle is 115–2d = 15. Then d=50, so the angles are 15, 65, 115, and 165.

Answer 2

The remaining angles are 65° , 115° , 165°

Given :

• The interior angles of a quadrilateral are in an AP

• The smallest angle is 15°

To find :

The remaining angles

Solution :

Step 1 of 2 :

Form the equation to find remaining angles

The interior angles of a quadrilateral are in an AP

The smallest angle is 15°

Ler common difference = d

So four interior angles of the quadrilateral are 15° , 15° + d , 15° + 2d , 15° + 3d

We know that sum of four interior angles of a quadrilateral is 360°

So by the given condition

15° + (15° + d) + (15° + 2d) + (15° + 3d) = 360°

Step 2 of 2 :

Calculate the remaining angles

15° + (15° + d) + (15° + 2d) + (15° + 3d) = 360°

⇒ 60° + 6d = 360°

⇒ 6d = 300°

⇒ d = 50°

∴ Four interior angles of the quadrilateral are 15° , 65° , 115° , 165°

Hence the remaining angles are 65° , 115° , 165°

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