Question

The angles of a quadrilateral are in the ratio 3: 4: 5 :6 What is the difference between the largest angle and the smallest angle?

Answer 1

Solution

Given :-

• Ratio of angles of a quadrilateral = 3:4:5:6

Find :-

• Difference between largey angle & smallest angle.

Explanation

We Have,

$\dag\boxed{\underline{\tt{\orange{\:Total\:angle\:of\:sum\:=\:360^{\circ}}}}}$

Let,

• First angle of quadrilateral = 3x
• Second angle of quadrilateral = 4x
• Third angle of quadrilateral = 5x
• Fourth angle of quadrilateral = 6x

So,

==> Total angle of quadrilateral= 360°

==> 3x+ 4x + 5x + 6x = 360

==> 18x = 360

==> x = 360/18

==> x = 20

Since,

• First angle of quadrilateral = 3×20 = 60°
• Second angle of quadrilateral = 4×20 = 80°
• Third angle of quadrilateral = 5×20 = 100
• Fourth angle of quadrilateral = 6×20 = 120°

Here,

• Largest angle of quadrilateral be = 120°
• Smallest angle of quadrilateral = 60°

Now, difference

==> Difference be = 120 - 60

==> Distance be = 60 °

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