Question

The angles of a quadrilateral are in the ratio of 2 : 3 : 5 : 8. Find the measure of
each angle.

Answer 1

Answer:

Ratio of the angles of quadrilateral = 2 : 3 : 5 : 8

Let, First angle be = 2x

Second angle be = 3x

Third angle be = 5x

Fourth angle be = 8x

Sum of these angles = 360°

So,

2x + 3x + 5x + 8x = 360°

=> 18x = 360°

=> x = 360°/18

=> x = 20°

First angle = 2 × 20° = 40°

Second angle = 3 × 20° = 60°

Third angle = 5 × 20° = 100°

Fourth angle = 8 × 20° = 160°

Ans. 40°, 60°, 100°, 160°

Hope it helps.

Answer 2

Answer:

$40^o,60^0,100^o,160^o$

Step-by-step explanation:

We will use the fact that the sum of angles of a quadrilateral is 360∘.

Sum of angles of quadrilateral is 360∘ ………(1)

Now, we have the ratio of angles as 2 : 3 : 5 : 8.

Let the first angle be $2x$, so then according to the ratio, the angles will be$2x,3x,5x,8x$

Now using (1), we will have:-

$2x+3x+5x+8x=360^o$

Simplifying the LHS, we will have:

$18x=360^o$

Taking the 15 from multiplication in LHS to division in RHS, we will have:-

$x=\frac{360}{18}=\frac{40}{2}=20^o$

Hence,$x=20^o$

So, the angles will be $40^o,60^0,100^o,160^o .$

∴ The smallest angle of the quadrilateral = 40 degrees

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