Question

The angles of a quadrilateral are in the ratio 1:2:3:4. The smallest angle is
(a) 72° (b) 144° (c) 36° (d) 18°​

Answer 1

Answer:

d)36°

Step-by-step explanation:

Let the smallest angle be x.

Therefore, all the angles will be x, 2x, 3x and 4x.

We know that,

Sum of all angles of quadrilateral is 360°.

x+2x+3x+4x. =360°

10x= 360°

x. =360/10

x. = 36°

The smallest angle is x= 36°

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Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

Option (c) 36°

The smallest angle of the Quadliateral is 36°.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Angles in the Quadliateral = 1 : 2 : 3 : 4

To find :

The smallest angle of the Quadliateral

Solution :

Consider the angles of the Quadliateral as :

• x
• 2x
• 3x
• 4x

As we know, the angles of the Quadliateral sum up and make 360°.

★ $\boxed{\sf{x + 2x + 3x+4x=360^{\circ}}}$

$\sf{\implies} \: x + 2x + 3x+4x=360^{\circ}$

$\sf{\implies} \: 10x = {360}^{\circ}$

$\sf{\implies} \: x = \dfrac{360}{10}$

$\sf{\implies} \: x = 36$

$\rule{300}{1.5}$

★ Value of 2x

$\sf{\implies} \: 36 \times 2$

$\sf{\implies} \: {72}^{\circ}$

★ Value of 3x

$\sf{\implies} \: 36 \times 3$

$\sf{\implies} \: {108}^{\circ}$

★ Value of 4x

$\sf{\implies} \: 36 \times 4$

$\sf{\implies} \: {144}^{\circ}$

The angles of the Quadliateral are 36°, 72°, 108°, and 144°

$\rule{300}{1.5}$

The smallest angle of the Quadliateral =

36 < 72 < 108 < 144

36 is the smallest Angle

$\therefore$ The smallest angle of the Quadliateral is 36°.

The answer is :

Option (c)

36°