Question

The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles

Answer 1

Answer:

The four angles of a quadrilateral are 75 ° , 85° , 95° and  105° .

Step-by-step explanation:

Given :  

Let the four angles of a quadrilateral be (a – 3d), (a – d), (a + d) and (a + 3d)

(a – 3d) + (a – d) + (a + d) + (a + 3d) = 360°

(sum of angles of quadrilateral)

4a = 360°

a = 90°

A.T.Q

(a + d) – (a – d) = 10° (Given)

a + d - a + d = 10°

2d = 10°

d = 5°

Therefore,

First angle,  (a – 3d) = 90° – 15° = 75°

Second angle, (a – d) = 90° – 5° = 85°

Third angle, (a + d) = 90° + 5° = 95°

Fourth angle, (a + 3d) = 90° + 15° = 105°

Hence, the four angles of a quadrilateral are 75 ° , 85° , 95° and  105° .

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Answer 2

Step-by-step explanation:

Let the one smallest angle of quadrilateral is x.

So the three angle (x+d) ; (x+2d) ; (x+3d)

The sum of interior angle of quadrilateral is 360°.

=> x +(x+d) + (x+2d) + (x+3d) =360°

=> 4x + 6×10= 360°

=> x = 300/4 = 75 °

Then, the angle of quadrilateral is 75° ; 85° ; 95° ; 105°.