Question

The angles of a quadrilateral are (5x), 5(x+2)°, (6x-20)° and 6(x+3)° respectively. Find (i) the value of x and (ii) each angle of the quadrilateral.​

Answer 1

Answer:

sum of the angles of a quadrilateral is 360°

so,

5x+5(x+2)+(6x-20)+6(x+3)=360

=> 5x+5x+10+6x-20+6x+18=360

=> 22x+8=360

=> 22x=360-8

=> 22x=352

=> x=352/22

=> x=176/11

=> x=16

I) value of x is 16

ii) 1st angle 5×16°=80°

2nd angle 5(16+2)°=5×18°=90°

3rd angle (6×16-20)°=(96-20)°=76°

4th angle 6(16+3)°=6×19°=114°

Answer 2

$\large\underline{\underline{\maltese{\red{\pmb{\sf{\: Given :-}}}}}}$

Angles of a quadrilateral are as follows :

• ➻ ∠1 = (5x) °
• ➻ ∠2 = 5(x+2)°
• ➻ ∠3 = (6x-20)°
• ➻ ∠4 = 6(x+3)°

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$\large\underline{\underline{\maltese{\gray{\pmb{\sf{\: To \: Find :-}}}}}}$

• ➻ Value of x = ?
• ➻ Angles of Quadrilateral = ?

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$\large\underline{\underline{\maltese{\purple{\pmb{\sf{\:Solution :-}}}}}}$

❒ As we know :

$\large\blue{\bigstar}{\underline{\boxed{\red{\sf{Angle\:Sum\:property{\small_{(Quadrilateral)}} = 360°}}}}}$

❒ Value of x :

$\: \: \: {:\longmapsto{\sf{ \: (5x)° + 5(x+2)° + (6x-20)° + 6(x+3)° = 360°}}}$

$\: \: \: {:\longmapsto{\sf{ \: (5x)° + 5x+10° + (6x-20)° + 6x+18° = 360°}}}$

$\: \: \: {:\longmapsto{\sf{ \: 22x° + 8 = 360°}}}$

$\: \: \: {:\longmapsto{\sf{ \: 22x° = 360° - 8}}}$

$\: \: \: {:\longmapsto{\sf{ \: 22x° = 352° }}}$

$\: \: \: {:\longmapsto{\sf{ \: x = \cancel\frac{352}{22} }}}$

$\large{\red{:\longmapsto}}{\underline{\overline{\boxed{\green{\sf{x = 16}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Angles of Quadrilateral :

$\leadsto{\sf{1st \: angle = (5x)°}}$

$\leadsto{\sf{ \: \: \: \: \: \: \: \: \: 5 \times 16°}}$

${:\longmapsto{\green{\underline{\sf{80°}}}}}$

$\leadsto{\sf{2nd \: angle = 5(x + 2)°}}$

$\leadsto{\sf{ \: \: \: \: \: \: \: \: \: 5(16 + 2)°}}$

$\leadsto{\sf{ \: \: \: \: \: \: \: \: \: 80 + 10°}}$

${:\longmapsto{\green{\underline{\sf{90°}}}}}$

$\leadsto{\sf{3rd \: angle = (6x - 20)°}}$

$\leadsto{\sf{ \: \: \: \: \: \: \: \: \: \: (6 \times 16 - 20)°}}$

$\leadsto{\sf{ \: \: \: \: \: \: \: \: \: \: (96 - 20)°}}$

${:\longmapsto{\green{\underline{\sf{76°}}}}}$

$\leadsto{\sf{4th \: angle = 6(x + 3)°}}$

$\leadsto{\sf{ \: \: \: \: \: \: \: 6(16 + 3)°}}$

$\leadsto{\sf{ \: \: \: \: \: \: \: 96 + 18°}}$

${:\longmapsto{\green{\underline{\sf{114°}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Verification :

${\twoheadrightarrow{\sf{ \: (5x)° + 5(x+2)° + (6x-20)° + 6(x+3)° = 360°}}}$

${\twoheadrightarrow{\sf{ \: (5 \times 16)° + 5(16+2)° + (6 \times 16-20)° + 6(16+3)° = 360°}}}$

${\twoheadrightarrow{\sf{ \: 80° + (80 + 10)° + (96-20)° + (96+18)° = 360°}}}</p><p>$

${\twoheadrightarrow{\sf{ \: 80° + 90° + 76° + 114° = 360°}}}</p><p>$

${\twoheadrightarrow{\sf{ \: 360° = 360°}}}</p><p>$

$\: \: \: \: \: \: \: \: \large{\red{\underline{\bf{LHS = RHS}}}}$

Hence , Verified.

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