Question

find the measure of each angle of a quadrilateral whose ratio of the angles is 1:2:3:4​

Answer 1

let the ratio be x

sum of the angles in a quadrilateral = 360 degree

1x + 2x + 3x + 4x = 360

10x=360

x=360/10

x=36

1x=1×36

=36 degree

2x=2×36

=72 degree

3x=3×36

=108 degree

4x=4×36

=144 degree

therefore, the angles are 36 degree,72 degree, 108 degree and 144 degree

Answer 2

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

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

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

$\rule{300}{1}$

Given :

The Ratio of angles = 1 : 2 : 3 : 4

To find :

The Measures of the angles in the quadliateral.

Solution :

Consider the angles as x, 2x, 3x, and 4x

As we know that the angles in the quadliateral sum up and make 360°.

★ Equation :

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

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

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

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

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

$\rule{300}{1}$

Value of 2x

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

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

$\rule{300}{1}$

Value of 3x

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

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

$\rule{300}{1}$

Value 4x

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

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

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

$\rule{300}{1}$

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

$\sf{\implies} \:72^\circ+108^\circ+144^\circ+36^\circ$

$\sf{\implies} \:360^\circ$

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