Question

the a
ngle of a quadrilateral are in ratio 3 ratio 5 ratio 9 ratio 13 find all the angle of the quadrilateral ​

Answer 1

✯✯ QUESTION ✯✯

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

━━━━━━━━━━━━━━━━━━━━

✰✰ ANSWER ✰✰

$\implies\tt{Let\:\angle{A}=3x}$

$\implies\tt{Let\:\angle{B}=5x}$

$\implies\tt{Let\:\angle{C}=9x}$

$\implies\tt{Let\:\angle{D}=13x}$

➮Sum of all the angles of a quadrilateral is 360°....

➥A.T.Q : -

$\implies\tt{\angle{A}+\angle{B}+\angle{C}+\angle{D}=360\degree}$

$\implies\tt{3x+5x+9x+13x=360\degree}$

$\implies\tt{30x=360\degree}$

$\implies\tt{x=\cancel\dfrac{360}{30}}$

$\implies\tt{\large{\boxed{\bold{\bold{\purple{\sf{x=12}}}}}}}$

➥Now ,

$\implies\tt{\angle{A}=3(12)}$

$\implies\tt\bold{36\degree}$

$\implies\tt{\angle{B}=5(12)}$

$\implies\tt\bold{60\degree}$

$\implies\tt{\angle{C}=9(12)}$

$\implies\tt\bold{108\degree}$

$\implies\tt{\angle{D}=13(12)}$

$\implies\tt\bold{156\degree}$

_______________________

✔VERIFICATION : -

$\implies\tt{3(13)+5(12)+9(12)+13(12)=360\degree}$

$\implies\tt{36+60+108+156=360\degree}$

$\implies\tt\bold{360\degree=360\degree}$

✺ HENCE VERIFIED ✺

Answer 2

Given:

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

Solution:

So, Let the angles of the quadrilateral

• 3 be 3x
• 5 be 5x
• 9 be 9x
• 13 be 13x

We know that,Sum of the angles of the quadrilateral = 360°

∴⠀⠀⠀ 3x + 5x + 9x + 13x = 360°

➟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 30x = 360°

➟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x = 360°/30

➟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x = 12°

So,

• 3x = 3 × 12° = 36°

• 5x = 5 × 12° = 60°

• 9x = 9 × 12° = 108°

• 13x = 13 × 12° = 156°

Hence, The angles of the quadrilateral are 36°, 60°, 108° and 156°

________________________________

⠀★ V E R I F I C A T I ON:

Sum of the angles of the quadrilateral = 360°

➟⠀⠀36° + 60° + 108° + 156° = 360°

➟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀360° = 360°

∴⠀⠀⠀⠀⠀⠀⠀⠀L.H.S = R.H.S

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Hence Verified!!