Question

solve This Please Fast
Find All The Angles Please​

Answer 1

Question:

If the angles of a quadrilateral are $\boldsymbol {(x + 10^{\circ}),\: (x + 30^{\circ}),\: (2x - 20^{\circ}),\: (2x - 38^{\circ})}$ find the angles of the quadrilateral.

Answer:

The angles are 73°, 93°, 106°, and 88°

Explanation:

Angle sum property of a quadrilateral says,

In a quadrilateral the sun of all interior angles is 360°

So,

${ \therefore \boldsymbol{(x + {10}^{ \circ} ) + (x + 30^{ \circ} ) + (2x - 20^{ \circ} ) + (2x - 38^{ \circ} )= 360^{ \circ} }}$

Solving for $\boldsymbol x$

${ \implies x + {10}^{ \circ} + x + 30^{ \circ} + 2x - 20^{ \circ} + 2x - 38^{ \circ} = 360^{ \circ} }$

${ \implies 6x + 40^{ \circ} - 58^{ \circ} = 360^{ \circ}}$

${ \implies 6x - 18^{ \circ} = 360^{ \circ}}$

${ \implies 6x = 360^{ \circ}} + 18^{ \circ}$

${ \implies 6x = 378^{ \circ}}$

${ \implies x = \dfrac{ 378^{ \circ}}{6}}$

${ \implies x = 63^{ \circ} }$

Hence, each angle would be:—

$\implies \: (x + 10^{ \circ}) = 73^{ \circ}$

$\implies \: (x + 30^{ \circ}) = 93^{ \circ}$

$\implies \: (2x - 20^{ \circ}) = 106^{ \circ}$

$\implies \: (2x - 38^{ \circ}) = 88^{ \circ}$

__________________________

Answer 2

Answer:

If the angles of a quadrilateral are \boldsymbol {(x + 10^{\circ}),\: (x + 30^{\circ}),\: (2x - 20^{\circ}),\: (2x - 38^{\circ})}(x+10

∘

),(x+30

∘

),(2x−20

∘

),(2x−38

∘

) find the angles of the quadrilateral.

Answer:

The angles are 73°, 93°, 106°, and 88°

Explanation:

Angle sum property of a quadrilateral says,

In a quadrilateral the sun of all interior angles is 360°

So,

{ \therefore \boldsymbol{(x + {10}^{ \circ} ) + (x + 30^{ \circ} ) + (2x - 20^{ \circ} ) + (2x - 38^{ \circ} )= 360^{ \circ} }}∴(x+10

∘

)+(x+30

∘

)+(2x−20

∘

)+(2x−38

∘

)=360

∘

Solving for \boldsymbol xx

{ \implies x + {10}^{ \circ} + x + 30^{ \circ} + 2x - 20^{ \circ} + 2x - 38^{ \circ} = 360^{ \circ} }.

x+10

∘

+x+30

∘

+2x−20

∘

+2x−38

∘

=360

∘

{ \implies 6x + 40^{ \circ} - 58^{ \circ} = 360^{ \circ}}⟹6x+40

∘

−58

∘

=360

∘

{ \implies 6x - 18^{ \circ} = 360^{ \circ}}⟹6x−18

∘

=360

∘

{ \implies 6x = 360^{ \circ}} + 18^{ \circ}⟹6x=360

∘

+18

∘

{ \implies 6x = 378^{ \circ}}⟹6x=378

∘

{ \implies x = \dfrac{ 378^{ \circ}}{6}}⟹x=

6

378

∘

{ \implies x = 63^{ \circ} }⟹x=63

∘

Hence, each angle would be:—

\implies \: (x + 10^{ \circ}) = 73^{ \circ}⟹(x+10

∘

)=73

∘

\implies \: (x + 30^{ \circ}) = 93^{ \circ}⟹(x+30

∘

)=93

∘

\implies \: (2x - 20^{ \circ}) = 106^{ \circ}⟹(2x−20

∘

)=106

∘

\implies \: (2x - 38^{ \circ}) = 88^{ \circ}⟹(2x−38

∘

)=88

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