Question

Four angles of the quadrilateralI in the ratio 3:4:5:6 find the angle

Answer 1

❒ Question:

• The angles of a quadrilateral are in the ratio of 3:4:5:6.

❒ To Find:

• The measure of each of the four angles

❒ Solution:-

Let all the angles of the quadrilateral be

• 3 = 3x
• 4 = 4x
• 5 = 5x
• 6 = 6x

As, we all know,

Sum of the angle of a quadilateral = 360°

$\tt \dashrightarrow 3x + 4x + 5x + 6x = 360 {}^{\circ}$

$\tt \dashrightarrow 18x = 360{}^{\circ}$

$\\ \tt \dashrightarrow x = \frac{360{}^{\circ} }{18}$

$\\ \tt \dashrightarrow x= 20{}^{\circ}$

Hence,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \circ \: \: \: \: \tt \:1st \: \: \: angle \: \: \: \: \: = 3x=3 \times 20=60{}^{\circ} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \circ \: \tt \:2nd \: \: \: angle \: \: \: \: \: = 4x=4 \times 20=80{}^{\circ} \: \: \: \: \: \\ \\ \circ \: \: \: \: \tt \:3rd \: \: \: angle \: \: \: \: \: =5x=5 \times 20=100 {}^{\circ} \\ \\ \circ \tt \: \:4th \: \: \: angle \: \: \: \: \: = 6x=6 \times 20=120 {}^{\circ}$

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Answer 2

Given:-

• Four angles of a quadrilateral are in the ratio 3:4:5:6

To Find:-

• The angles

Solution:-

$\sf Let~the~angles~be \begin{cases}\sf ★ \; 3x \\ \sf ★ \;4x \\ \sf ★ \; 5x \\ \sf ★\; 6x \end{cases}$

ATQ:-

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

By angle sum property:-

$\sf \dashrightarrow{3x + 4x +5x +6x =360°}$

$\sf \dashrightarrow{7x + 11x =360°}$

$\sf \dashrightarrow{18x =360°}$

$\large\sf \dashrightarrow{x = \frac{360}{18}}°$

$\large\sf \dashrightarrow{x =\cancel \frac{360}{18}}°$

$\underline {\boxed { \star \: {\frak{ \pmb {x=20°}}}}}$

∴ The angles are:-

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