Question

in a quadrilateral and the angles are in the ratio 1:2:4:5find the measure of each angle of the quadrilateral​

Answer 1

Answer:

30 degrees, 60 degrees, 120 degrees, 150 degrees

Step-by-step explanation:

Ratio of angles = 1:2:4:5

Let x be the common ratio

Thus, the angles are 1x,2x,4x and 5x

Sum of angles in a quadrilateral = 360 degrees

1x+2x+4x+5x = 360

12x = 360

x = 360/12 = 30

The measure of each angle respectively are = x,2x,4x,5x = 30, 30*2, 30*4, 30*5 = 30,60,120,150

Answer 2

Given that,

• The ratio of angles in a quadrilateral are 1:2:4:5.

◾️We need to find the measures of each angle.

____________

To do so,

let's assume m be the common factor of all the angles.

Then the angles will be -

• first angle will be 1m = m.
• Second angle will be 2m.
• Third angle will be 4m.
• And Fourth angle will be 5m.

And we knew that quadrilateral is a polygon/shape of 4 sides and 4 angles.

And $\large{\boxed{\sf{\orange{Angle\:sum\:property_{(quadrilateral)} = 360°}}}}$

Let's start solving question!

According to this question,

$\displaystyle{\sf{m+2m+4m+5m=360°}}$

:$\implies{\sf{12m=360°}}$

:$\implies{\sf{m=\dfrac{360°}{12}}}$

:$\implies{\sf{m=30°}}$

Therefore, If m = 30°, then the other angles will be,

• $\large{\overbrace{\sf{\pink{First\:angle= 30°}}}}$
• $\large{\sf{\pink{Second\:angle = 60°}}}$
• $\large{\sf{\pink{Third\:angle= 120°}}}$
• $\large{\underbrace{\sf{\pink{Fourth\:angle= 150°}}}}$

And we are done! :D

__________________________