Question

2. The four angles of a quadrilateral
are in the ratio 3:4:5:6. Find the angles.
​

Answer 1

Answer:

let 3x +4x +5x +6x = 180

18x = 180

x = 180/18

x = 10

angle 1 = 3(10) = 30

2 = 4×10 = 40

3 =5×10 = 50

4 = 6× 10 = 60

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Answer 2

When the word quadrilateral is specified ; we must understand that the sum of all angles is 360°.

So let's take the common angle as x.

Now we will consider ratios in x form and make the whole equal to 360°.

$\small{\longrightarrow{\sf{3x + 4x + 5x + 6x = 360}}}$

$\small{\longrightarrow{\sf{18x = 360}}}$

$\small{\longrightarrow{\sf{x = \dfrac{360}{18}}}}$

$\small{\longrightarrow{\sf{x = \cancel{\dfrac{360}{18}} \implies 20}}}$

So the common angle is 20°

For finding the angles we need to just multiply the ratios while substituting x.

$\small{\longrightarrow{\sf{3x = 3 \times 20 = \angle 60}}}$

$\small{\longrightarrow{\sf{4x = 4 \times 20 = \angle 80}}}$

$\small{\longrightarrow{\sf{5x = 5 \times 20 = \angle 100}}}$

$\small{\longrightarrow{\sf{6x = 6 \times 20 = \angle 120}}}$

Verification :

If we add up the angles we have found the sum must be equal to 360.

$\small{\longrightarrow{\sf{60 + 80 + 100 + 120 = 360}}}$

$\small{\longrightarrow{\sf{140 + 220 = 360}}}$

$\small{\longrightarrow{\sf{360 = 360}}}$

LHS = RHS