Question

three angles of a quadrilateral are 100°, 90°and110° ​

Answer 1

Accomplished Question :

›»› Three angles of a quadrilateral are 100°, 90° and 110°, then find the third angle of a quadilateral.

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AnswEr :

• The third angle of a quadrilateral = 60°.

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Step-by-step explanation :

We are given with the three angles of a quadrilateral, that is,

• 100°, 90° and 110°.

We have to find out the third angle of a quadrilateral.

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Now,

Let us consider that, the third angle of a quadrilateral is "x".

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As we know that

The sum of all four angles of a quadrilateral is 360°. This statement is known as 'angle sum property of a quadrilateral'.

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Substituting the given angles in the formula, we

get :

⇒ 100 + 90 + 110 + x = 360

⇒ 190 + 110 + x = 360

⇒ 300 + x = 360

⇒ x = 360 - 300

⇒ x = 60

Hence, the third angle of a quadrilateral is 60°.

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Verification :

The sum of all four angles of a quadrilateral is 360°.

⇒ 100 + 90 + 110 + 60 = 360

⇒ 190 + 110 + 60 = 360

⇒ 300 + 60 = 360

⇒ 360 = 360

Clearly, LHS = RHS.

Here both conditions satisfy, so our answer is correct$.$

Hence Verified !

Answer 2

Answer:

Given :-

• Three angle of Quardilateral = 100⁰,90⁰,110⁰

To Find :-

Fourth angle

Solution :-

Let the fourth angle of Quardilateral be x.

As we know that sum of all sides of Quardilateral is 360⁰.

$\sf \: 100 + 90 + 110 + x = 360$

$\sf \: 190 + 110 + x = 360$

$\sf \: 300 + x = 360$

$\sf \: x = 360 - 300$

$\sf \: x = 60$

Hence,

The fourth angle is 60⁰.

Let's verify :-

$\sf \: 100 + 90 + 110 + 60 = 360$

$\sf \: 190 + 170 = 360$

$\sf \: 360 = 360$

Hence verified