Question

the angle of a quad. in the ratio3:4:5:6 then difference between smallest and largest angle is

a. 40°
b. 120°
c. 45°
d. 60°​

Answer 1

Answer:

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of which book it is of which class

Answer 2

★GIVEN★

The angles of a quad. is in the ratio 3:4:5:6.

★To Find★

Difference between the largest and smallest angle.

★SOLUTION★

We know that sum of all angles of a quadrilateral is 360°.

Let the angles be 3x, 4x, 5x, 6x.

According to the question,

$\large\implies{\sf{3x+4x+5x+6x=360}}$

$\large\implies{\sf{18x=360}}$

$\large\implies{\sf{x=\dfrac{360}{18}}}$

$\large\implies{\sf{x=\dfrac{\cancel{360}}{\cancel{18}}}}$

$\large\therefore\boxed{\bf{x=20.}}$

The angles are,

1. 2x = 2 × 20 = 40°
2. 3x = 3 × 20 = 60°
3. 4x = 4 × 20 = 80°
4. 5x = 5 × 20 = 100°

★VERIFICATION★

$\large\implies{\sf{40+60-80+100=360}}$

$\large\implies{\sf{360=360}}$

$\large\therefore\boxed{\bf{LHS=RHS}}$

So,

• The smallest angle is 40°.
• The largest angle is 100°.

Difference between largest and smallest angle = 100° - 40° = 60°

$\large{\green{\underline{\boxed{\bf{Difference\:between\:largest\:and\:smallest\:angle\:is\:60\degree.}}}}}$