Question

Angle of quadrilateral are in ap and common difference if 10 find angles

Answer 1

Question:

Angles of a quadrilateral are in AP and the common difference is 10°. Then find the angles.

Answer:

75° , 85° , 95° and 105°

Notes:

• A polygon of four sides is called quadrilateral.

• The sum of its all the four interior angles is 360°.

• An AP is a sequence in which the difference between the consecutive terms are same.

• The terms of an AP is given as ;

a , (a+d) , (a+2d) , (a+3d) , .......

where "a" is the first term and "d" is the common difference of the AP.

Solution:

It is given that,

The angles of a quadrilateral are in AP with common difference 10°.

Thus,

Let the four angles of the quadrilateral as , a , (a+10°) , (a+2•10°) , (a+3•10°)

ie; a , (a+10°) , (a+20°) , (a+30°)

Also,

We know that,

The sum of all the four interior angles of a quadrilateral is equal to 360°

Thus,

=> a + (a+10°)+ (a+20°)+ (a+30°) = 360°

=> 4a + 60° = 360°

=> 4a = 360° - 60°

=> 4a = 300°

=> a = 300°/4

=> a = 75°

Hence,

The four angles of the quadrilateral are

75° , 85° , 95° and 105°

Answer 2

Answer

GiveN

Angle of quadrilateral are in ap and common difference if 10.

To FinD

Find the angles of quadrilateral.

HencE

Let the following be the four angles of the quadrilateral:-

= ( M ) , (M + 10°) , (M + 2 × 10°) , (M + 3 × 10°)

= ( M ) , ( M + 10° ) , ( M + 20° ) , ( M + 30° )

All the interior angles of quadrilateral = 360°

$\bf = M + ( M + 10° ) + ( M + 20° ) + (M + 30° ) = 360° \\ </p><p>\bf = 4M + 60° = 360° \\ </p><p>\bf = 4M = 360° - 60° \\ </p><p>\bf = 4M = 300°$

$\bf = M = \frac{300°}{4} \\ </p><p>\bf = M = 75°$

Finding 1 we get all other three.

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