Question

Two angles of a quadrilateral measure 190° and 40°. The other two angles are in a ratio of 5:8. What are the measures of those two angles

Answer 1

Solution :

Let the 3rd angle be 5x and 4th angle be 8x

★ Sum of all angles of Quadrilateral = 360°

According to the question :

→ 190° + 40° + 5x + 8x = 360°

→ 230° + 13x = 360°

→ 13x = 360° - 230°

→ 13x = 130°

→ x = $\sf\cancel\dfrac{130}{13}$

→ x = 10°

$\therefore$ Fourth angle = 5(10) = 50° and Fifth angle = 8(10) = 80°

Verification :

★ Sum of all angles of Quadrilateral = 360°

→ 190° + 40° + 5(10) + 8(10) = 360°

→ 230° + 50° + 80° = 360°

→ 280° + 80° = 360°

→ 360° = 360°

Hence,Verified!

Answer 2

✯✯ QUESTION ✯✯

Two angles of a quadrilateral measure 190° and 40°. The other two angles are in a ratio of 5:8. What are the measures of those two Angles..

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✰✰ ANSWER ✰✰

$\longmapsto\tt{1st\:Angle=190\degree}$

$\longmapsto\tt{2nd\:Angle=40\degree}$

$\longmapsto\tt{Let\:3rd\:Angle\:be=5x}$

$\longmapsto\tt{Let\:4th\:Angle\:be=8x}$

$\longmapsto\tt\bold{Sum\:of\:angles\:of\:Quadrilateral=360\degree}$

➥A.T.Q : -

$\longmapsto\tt{190\degree+40\degree+5x+8x=360\degree}$

$\longmapsto\tt{230\degree+13x=360\degree}$

$\longmapsto\tt{13x=360\degree-230\degree}$

$\longmapsto\tt{13x=130}$

$\longmapsto\tt{x=\cancel\dfrac{130}{13}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{x}\orange{=}\purple{10}}}$

➥Now ,

$\longmapsto\tt{3rd\:Angle=5(10)}$

$\longmapsto\tt\bold{50\degree}$

$\longmapsto\tt{4th\:Angle=8(10)}$

$\longmapsto\tt\bold{80\degree}$

_______________________

✔VERIFICATION : -

$\longmapsto\tt{190\degree+40\degree+50\degree+80\degree=360\degree}$

$\longmapsto\tt{360\degree=360\degree}$

$\pink\longmapsto\:\large\underline{\boxed{\bf\red{L.H.S}\orange{=}\orange{R.H.S}}}$

✺ HENCE VERIFIED ✺