Question

The angles of a quadrilateral are in A.P. with common difference 20°.Find it's angles.

Answer 1

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GIVEN THAT,

The angles of quadrilateral are in A.P.
with common difference , d = 20°

Let the first angle be 'a'

Then,

Second angle = a+d = a+20°

Third angle = a+2d = a+40°

Fourth angle = a+3d = a+60°

Now,

We know that

Sum of all angles of quadrilateral is 360°

=> a + a+20° + a+40° + a+60° = 360°

=> 4a + 120° = 360°

=> 4a = 360°-120°

=> 4a = 240°

=> a = 240°/4

=> a = 60°

First angle = 60°

Second angle = 60°+20° = 80°

Third angle = 60°+40° = 100°

Fourth angle = 60°+60° = 120°

HENCE,

The angles of given quadrilateral are
60° , 80° , 100° , 120°

Answer 2

The angles are 60, 80, 100, 120 Degrees.

The number of sides that are there in a quadrilateral = 4 sides

The sum of total number of sides in a quadrilateral = 360 Degrees

Common Difference of the AP (d) = 20

Let us assume the angles of the quadrilateral to have the angles:

x

x + 20

x + 40

x + 60

Adding all the angles together:

=> x + x + 20 + x + 40 + x + 60 = 360

=> 4 x + 120 = 360

=> 4 x = 360 - 120

=> 4 x =  240

=> x = 240 / 4

=> x = 60

First Angle: The value of x is 60 Degrees

Second Angle: The Value of x + 20 is 60 + 20 = 80 Degrees

Third Angle: The Value of x + 40 is 60 + 40 = 100 Degrees

Fourth Angle: The Value of x + 60 is 60 + 60 = 120 Degrees

Therefore, the angles are 60, 80, 100, 120 Degrees.