Question

57. The angles of a quadrilateral are in the
ratio 3:7:9:11. Find all the angles :
(A) 36°, 84°, 108°, 132
(B) 90°, 60°, 100°, 110°
(C) 30°, 70°, 90°, 120°
(D) None of these.​

Answer 1

Answer:

Given :-

• The angles of a quadrilateral are in the ratio of 3 : 7 : 9 : 11.

To Find :-

• What are the angles.

Solution :-

Let,

➲ First Angle = 3x

➲ Second Angle = 7x

➲ Thrid Angle = 9x

➲ Fourth Angle = 11x

As we know that :

★ Sum Of All Angles Of A Quadrilateral = 360°

According to the question by using the formula we get,

↦ 3x + 7x + 9x + 11x = 360°

↦ 10x + 9x + 11x = 360°

↦ 19x + 11x = 360°

↦ 30x = 360°

↦ x = 360°/30

➠ x = 12°

Hence, the required angles of quadrilateral are :

❒ First Angle :

⇒ First Angle = 3x

⇒ First Angle = 3(12°)

➦ First Angle = 36°

❒ Second Angle :

⇒ Second Angle = 7x

⇒ Second Angle = 7(12°)

➦ Second Angle = 84°

❒ Third Angle :

⇒ Third Angle = 9x

⇒ Third Angle = 9(12°)

➦ Third Angle = 108°

❒ Fourth Angle :

⇒ Fourth Angle = 11x

⇒ Fourth Angle = 11(12°)

➦ Fourth Angle = 132°

∴ The angles of quadrilateral are 36°, 84°, 108° and 132° respectively.

Hence, the correct options is option no (A) 36°, 84°, 108°, 132°.

VERIFICATION :-

↦ 3x + 7x + 9x + 11x = 360°

By putting x = 12° we get,

↦ 3(12°) + 7(12°) + 9(12°) + 11(12°) = 360°

↦ 36° + 84° + 108° + 132° = 360°

➠ 360° = 360°

Hence, Verified.

Answer 2

$\underline\green{\underline{\sf{\maltese\: Given\::-}}}$

$\purple\dashrightarrow$The angles of a quadrilateral are in the ratio 3:7:9:11

$\underline\green{\underline{\sf{\maltese\: To\:Find\::-}}}$

$\purple\dashrightarrow$The measure of all the angles.

$\underline\green{\underline{\sf{\maltese\: Solution\::-}}}$

We know that,

Sum of all the angles of a quadrilateral = 360°

Let,

$\red\rightsquigarrow$the first angle = 3x

$\red\rightsquigarrow$the second angle = 7x

$\red\rightsquigarrow$the third angle = 9x

$\red\rightsquigarrow$the fourth angle = 11x

Then,

$\implies$$\sf{3x + 7x + 9x + 11x = 360°}$

$\implies$$\sf{30x = 360°}$

$\implies$$\sf{x= \frac{360}{30}}$

$\implies$$\sf{x = 12}$

∴ the measure of,

$\tt{the\:first \:angle = 3x = 3 × 12 = 36°}$

$\tt{the \:second \:angle = 7x = 7 × 12 = 84°}$

$\tt{the\: third\: angle = 9x = 9 × 12 = 108°}$

$\tt{the\: fourth \:angle = 11x = 11 × 12 = 132°}$

Hence, (A)36°, 84°, 108°, 132°is the correct answer.

Hope it helps :)