Question

the angles of quadrilateral are in the ratio 3:4:5:6. find all the angles of the quadrilateral?
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Answer 1

Given that angles of a quadrilateral are in the ration 3:4:5:6.

We know that sum of all angles of a quadrilateral =360

0

.

So, angles of quadrilateral are:

∠A=

18

3

×360=60,∠B=

18

4

×360=80,∠C=

18

5

×360=100,∠D=

18

6

×360=120

Now from figure, we have

∠A+∠D=60+120=180

i.e. sum of interior angles on the same side of the transversal AD=180

0

.

Therefore, AB∥DC

Hence, the given quadrilateral is a trapezium.

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Answer 2

Answer:

let the common ratio be x

$</p><p>3x + 4x + 5x + 6x = 360⁰ ( angle sum property) \\ </p><p>18x = 360⁰ \\ X = 360 \div 18 \\ </p><p>X = 20 \\ </p><p>3x = 20 \times 3 = 60 \degree \\ </p><p>4x = 20 \times 4 = 80 \degree \\ </p><p>5x = 20 \times 5 = 100 \degree \\ </p><p>6x = 20 \times 6 = 120 \degree$