Question

The angle of a quadrilateral are in the ratio of 1:2:4:5. What are the measures of each of the Angles?

Answer 1

Step-by-step explanation:

Let the measure of angles be x,2x,3x and 4x.

We know that sum of measure of all four angles is 360 degree

.

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

⇒ 10x=360

⇒ x=36

now put x= 36 on 2x,3x4x

⇒ 2x=2×36

=72

⇒ 3x=3×36

=108

⇒ 4x=4×36

=144

⇒ The measures of angles of quadrilateral are 36

,72

,108

and 144

⇒ We can see measure of all 4 angles are different so, the given quadrilateral is trapezium.

Answer 2

$\huge{\fbox{\red{A}{\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}{\tt}}$

$\huge\mathtt\orange{Given:-}$

The angle of a quadrilateral are in the ratio of 1:2:4:5.

$\huge\mathtt\pink{To\:find :-}$

Measure of each angle of quadrilateral

$\huge\mathtt\gray{Solution:-}$

Let the angles of the quadrilateral be 1x , 2x , 4x , 5x.

As we know that,

The sum of the angles of the quad. = 360°

So, 1x + 2x + 4x + 5x = 360°

12x = 360°

$x = \frac{360°}{12}$

x = 30°

Therefore,

1x = 1(30) = 30°

2x = 2(30) = 60°

4x = 4(30) = 120°

5x = 5(30) = 150°

$\bold{\fbox{\color{blue}{Hope \:its\:helpful\:♡♡}}}$