Question

the ratio of the angle P,Q,R and s of a quadrilateral pqrs is 3:6:4:5,find the measure of each angle ​

Answer 1

• GIVEN:-

The ratio of the angle P,Q,R and S of a quadrilateral PQRS is 3:6:4:5.

• To Find:-

Find the measure of each angle.

• SOLUTION:-

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

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

According to the question,

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

$\large\Longrightarrow{\sf{360\degree=16x}}$

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

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

$\large\therefore\boxed{\sf{x=20}}$

So the angles are:-

1. 3x = 3 × 20 = 60°
2. 6x = 6 × 20 = 120°
3. 4x = 4 × 20 = 80°
4. 5x = 5 × 20 = 100°

• Now let's verify it:-

$\large\Longrightarrow{\sf{360\degree=60\degree+120\degree+80\degree+100\degree}}$

$\large\Longrightarrow{\sf{360\degree=360\degree}}$

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

Hence verified.

$\large\purple\therefore\boxed{\sf{\purple{The\:angles\:are\:60\degree,\:120\degree,\:80\degree,\:100\degree.}}}$