Question

if the interrior angles of quadrilateral are in ratio 6:5:4:3 then find the measure of each angle​

Answer 1

$\huge\bold{\mathtt{Question⇒}}$

If the interrior angles of quadrilateral are in ratio 6:5:4:3, then find the measure of each angle.

$\huge\bold{\mathtt{Given⇒}}$

The interrior angles of quadrilateral are in ratio 6:5:4:3.

$\huge\bold{\mathtt{To\:find⇒}}$

The measure of the angles.

$\huge\bold{\mathtt{Solution⇒}}$

Let the angles are 6x°, 5x°, 4x° and 3x°.

We know that:

The sum of all angles of a quadrilateral = 360°.

So we can say-

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

➳ 18x = 360

Divide both sides by 18.

➳ 18x ÷ 18 = 360 ÷ 18

➳ x = 20

$\huge\bold{\mathtt{Hence⇒}}$

x = 20

Substitute x with 20.

• 6x° = (6 × 20)° = 120°
• 5x° = (5 × 20)° = 100°
• 4x° = (4 × 20)° = 80°
• 3x° = (3 × 20)° = 60°

$\huge\bold{\mathtt{Therefore⇒}}$

The angles are 120°, 100°, 80° and 60°.

$\huge\bold{\mathtt{Confused??}}$

$\huge\bold{\mathtt{Verification⇒}}$

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

➳ 120 + 100 + 80 + 60 = 360

➳ 360 = 360

So, L.H.S = R.H.S.

Hence, verified.

$\huge\bold{\mathtt{Done}}$

$\large\bold{\mathtt{Hope\:this\:helps\:you.}}$

$\large\bold{\mathtt{Have\:a\:nice\:day.}}$