Question

the ratio of the angles of a quadrilateral is 1 isto 2 isto 3 isto 4 then the measure of the smallest angle​

Answer 1

Answer:

Appropriate Question :-

• The ratio of the angles of a quadrilateral is 1 : 2 : 3 : 4, then find the measure of the smallest angle.

Given :-

• The ratio of the angles of a quadrilateral is 1 : 2 : 3 : 4.

To Find :-

• What is the measure of the smallest angle.

Solution :-

Let,

• First angle = x
• Second angle = 2x
• Third angle = 3x
• Fourth angle = 4x

As we know that :

★ Sum of all angles of interior angle of quadrilateral = 360° ★

According to the question by using the formula we get,

↦ x + 2x + 3x + 4x = 360°

↦ 3x + 7x = 360°

↦ 10x = 360°

↦ x = 360°/10

➠ x = 36°

Hence, the required angles of a quadrilateral are :

✪ First angle of a quadrilateral :

⇒ x

➦ 36°

✪ Second angle of a quadrilateral :

⇒ 2x

⇒ 2(36°)

⇒ 2 × 36°

➦ 72°

✪ Third angle of a quadrilateral :

⇒ 3x

⇒ 3(36°)

⇒ 3 × 36°

➦ 108°

✪ Fourth angle of a quadrilateral :

⇒ 4x

⇒ 4(36°)

⇒ 4 × 36°

➦ 144°

Hence, the measure of the all angles of a quadrilateral is 36°, 72°, 108° and 144° respectively.

∴ The measure of the smallest angle of a quadrilateral is 36°.

VERIFICATION :

↦ x + 2x + 3x + 4x = 360°

By putting x = 36° we get,

↦ x(36°) + 2(36°) + 3(36°) + 4(36°) = 360°

↦ 36° + 72° + 108° + 144° = 360°

➲ 360° = 360°

Hence, Verified.

$\rule{150}{2}$

#Learn more :

Q.2.A. The angles of a quadrilateral are in the following ratio. Find the measurements of the angles.

a) 2:3:4:6

https://brainly.in/question/38919789

Answer 2

$\bf{Given}$

$\tt{Ratio \: \: of \: \: the \: \: angles \: \: of \: \:a \: \: Quadrilateral \: \:is \: \: 1:2:3:4 }$

$\bf{Then}$

$\tt{Let \: \: the \: \: ratio \: \: be \: \: x , 2x , 3x \: \: and \: \: 4x }$

$\tt{As \: \: we \: \: know \: \: that}$

$\tt{Sum \: \: of \: \: all \: \: angles \: \: of \: \: Quadrilateral \: \: is \: \: 360⁰}$

$\tt ⟶ x + 2x + 3x + 4x = 360$

$\tt⟶ x + 9x = 360$

$\tt⟶ 10x = 360$

$\tt⟶ x = 360/10$

$\tt ⟶ x = 36⁰$

$\tt{Now \: ,we \: \: have \: \: to \: \: find \: \: the \: \: smallest \: \: angle }$

$\tt{x = 36⁰}$

$\tt{2x = 2(36) = 72⁰}$

$\tt{3x = 3(36) = 108⁰}$

$\tt{4x = 4(36) = 144⁰}$

$\bf{Hence \:,Smallest \:angle \: is \: 36⁰}$