Question

The three angles of
quadrilateral, are in
ratio 3:4;5:6 calculate the angles​

Answer 1

Correct Question,

The 4 angles of a quadrilateral are in the ratio 3:4:5:6. Calculate the measure of each angle.

Answer:

Let the angles be 3x, 4x, 5x and 6x.

We know that as per the angle sum property of quadrilaterals, the sum of all the angles of a quadrilateral is 360 degrees.

Therefore, we can write it down as:

3x + 4x + 5x + 6x = $360^o$

18x = $360^o$

So,

x = 360/18 = 20

→ Measure of angle 1 = 3x = 3 x 20 = 60 degrees

→ Measure of angle 2 = 4x = 4 x 20 = 80 degrees

→ Measure of angle 3 = 5x = 5 x 20 = 100 degrees

→ Measure of angle 4 = 6x = 6 x 20 = 120 degrees

Statement

Therefore the measure of the 4 angles of the quadrilateral are $60^o,80^o,100^o,120^o$.

Answer 2

Answer:

$\mathsf{Given}$

$\mathsf{Angles \: are \: in \: the \: ratio \: 3:4:5:6}$

$\mathsf{Let \: the \: angles \: be \: 3x , 4x , 5x , 6x}$

$\mathsf\red{■}$ We know sum of angles in quadrilateral = 360°

$\mathsf{So}$

$\mathsf{3x+4x+5x+6x \: = \: 360}$

$\mathsf{18x \: = \: 360}$

$\mathsf{x \: = \: \frac{360}{18}}$

$\mathsf{x \: = \: 20}$

$\mathsf\blue{3x \: = \: 3 \times 20 \: = \: 60°}$

$\mathsf\blue{4x \: = \: 4 \times 20 \: = \: 80°}$

$\mathsf\blue{5x \: = \: 5 \times 20 \: = \: 100°}$

$\mathsf\blue{6x \: = \: 6 \times 20 \: = \: 120°}$

$\mathsf\red{\therefore \: the \: angles \: are \: :- \: 60°;\: 80°; \: 100°; \: 120°}$