Question

the ratio of the angles of a quadrilateral is 3:5:9:13 ,find all the angles ofthis quadrilateral​

Answer 1

Given:

• The ratio of the angles of a quadrilateral is 3:5:9:13

To Find:

• All angles of Quadrilateral

Solution:

• As here in the Question we known the ratio of angles of Quadrilateral. So, Let the Angles be 3x, 5x,9x and 13x. We know that sum of all angles of Quadrilateral is 360°

Let,

• 1st angle = 3x
• 2nd angle = 5x
• 3rd angle = 9x
• 4th angle = 13x

According to the Question :

• Sum of all angles of Quadrilateral = 360°
• 3x + 5x + 9x + 13x = 360°
• 8x + 9x + 13x = 360°
• 30x = 360°
• x = 360/30
• x = 12

So, Required angles are:

• 1st angle = 3x = 3 × 12 = 36°
• 2nd angle = 5x = 5 × 12 = 60°
• 3rd angle = 9x = 9 × 12 = 108°
• 4th angle = 13x = 13 × 12 =156°

Therefore, Angles of Quadrilateral are 36°, 60° , 108° and 156°

━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

❒ Question:

• The angles of a quadrilateral are in the ratio of 3:5:9:13.

❒ To Find:

• The measure of each of the four angles

❒ Solution:-

Let all the angles of the quadrilateral be

• 3 = 3x
• 5 = 5x
• 9 = 9x
• 13 = 13x

As, we all know,

Sum of the angle of a quadilateral = 360°

$\tt ⇛ 3x + 5x + 9x + 13x = 360 {}^{\circ}$

$\tt ⇛ 30x = 360{}^{\circ}$

$\\ \tt ⇛ x = \frac{360{}^{\circ} }{30}$

$\\ \tt ⇛ x= 12{}^{\circ}$

Hence,

$\begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \circ \: \: \: \: \tt \:1st \: \: \: angle \: \: \: \: \: = 3x=3 \times 12=36{}^{\circ} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \circ \: \tt \:2nd \: \: \: angle \: \: \: \: \: = 5x=5 \times 12=60{}^{\circ} \: \: \: \: \: \\ \\ \circ \: \: \: \: \tt \:3rd \: \: \: angle \: \: \: \: \: =9 x=9 \times 12=108 {}^{\circ} \\ \\ \circ \tt \: \:4th \: \: \: angle \: \: \: \: \: = 13x=13 \times 12=156 {}^{\circ} \\ \\ \end{gathered} </p><p>$

________________________________________

❍ V E R I F I C A T I O N:

Sum of the angle of the quadrilateral = 360°

$\tt⇛3x + 5x + 9x + 13x = 360 {}^{\circ}$

$\tt⇛36{}^{\circ} + 60{}^{\circ} + 108{}^{\circ} + 156{}^{\circ}= 360{}^{\circ}$

$\tt⇛360{}^{\circ} = 360{}^{\circ}$

$\quad \quad{ \textbf{ \textsf { \quad{L. H. S = R. H. S}}}}$