Question

53. 13. The four angles of a quadrilateral
are in the ratio 2:3:5:8. Find the angles.
(a) 40°, 60°,100°,160°
(b) 50°,70°, 90°,150°
(c) 40°,60°, 110°,150°
(d) 40°,50°, 100°,170°
Full Marks : 1​

Answer 1

Step-by-step explanation:

$sum \: of \: angles \: of \: a \: quadilateral = 360 \\ let \: angles \: be \: 2x \: 3x \: 5x \: 8x \\ so \: 2x + 3x + 5x + 8x = 360 \\ 18x = 360 \\ x = 20$

$therefore \: angles \: of \: the \: given \: quad. \: are \: as \: under$

$2 \times 20 = 40 \\ 3 \times 20 = 60 \\ 5 \times 20 = 100 \\ 8 \times 20 = 160$

Answer 2

☆ Solution ☆

Given :-

• The four angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8.

To Find :-

• The angles of quadrilateral.

Step-by-Step-Explaination :-

Let the ratios be 2x, 3x, 5x and 8x

As we know that :-

The sum of the angles of a quadrilateral is 360° .

So,

2x + 3x + 5x + 8x = 360°

18x = 360°

x = 360/18

x = 20°

Thus,

The measure of all angles of the quadrilateral are :-

2x = 2 × 20 = 40°

3x = 3 × 20 = 60°

5x = 5 × 20 = 100°

8x = 8 × 20 = 160°

Hence,

Option a) 40°, 60°, 100°, 160° is correct option.