Question

PLEASE solve the problem. ​

Answer 1

Given,

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

To find,

Least angle of quadrilateral.

Solution :

Let the angles of quadrilateral be a, (a + d), (a + 2d) and (a + 3d)

Common difference , d = 10°

Now atq,

⇒ a + (a + d) + (a + 2d) + (a + 3d) = 360°

⇒ a + a + d + a + 2d + a + 3d = 360°

⇒ 4a + 6d = 360°

⇒ 4a + 6(10) = 360°

⇒ 4a + 60 = 360°

⇒ 4a = 360° - 60°

⇒ 4a = 300°

⇒ a = 300°/4

⇒ a = 75°

Therefore,

Least angle of quadrilateral = 75°

Answer 2

$\huge{\boxed{\rm{Question}}}$

The angle of quadrilaterals are in A.P whose common difference is 10. Find the least angle.

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• The angle of quadrilaterals are in A.P whose common difference is 10.

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• Least angle.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• Least angle = 75 degrees.

$\large{\boxed{\boxed{\sf{Assumptions}}}}$

• Let the angle of the quadrilateral are x , ( x + y ) , ( x + 2y ) , ( x + 3y )

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

• This question says that there is a quadrilateral and the angle of that quadrilateral are in A.P whose common difference is 10. Afterwards it ask us to find the least angle of this quadrilateral.

$\large{\boxed{\boxed{\sf{How \: to \: solve \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Let's \: see \: the \: procedure \: now}}}}$

• To solve this question we fave to use out taken assumptions afterthat using the assumptions we have to put the values and find them properly. Afterwards we get our final result that is 75°

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

• x , ( x + y ) , ( x + 2y ) , ( x + 3y ) = 360°

• x + x + y + x + 2y + x + 3y = 360°

• x + x + x + x + y + 2y + 3y = 360°

• 4y + 6y = 360°

• 4y + 6(10) = 360°

• 4y + 60 = 360°

• 4y = 360 - 60

• 4y = 300

• y = 300/4

• y = 150/2

• y = 75°

Hence, y = 75°

Means, least angle of quadrilateral = 75°

Note : We write 360° after equal to sign because the sum of the interior angles of quadrilateral will be 360°