Question

the angle of a quadrilateral are x degrees, (x+15 degrees) (x+25 degrees) and (x+4) find the angles ​

Answer 1

Answer:

Step-by-step explanation:

We need to know the following things before we answer this question.

The sum of all angles of a quadrilateral is equal to 360°, whatever the consequences be.

So, we are given the following :-

• Angles are x
• x+15
• x+25
• x+4

Now, refer to the attachment and find something. I have mentioned a trick there.

Applying the trick, we can solve it further.

$\implies$ x+x+15+x+25+x+4 = 360

$\implies$ 4x+44 = 360

$\implies$ 4x = 360 - 44

$\implies$ 4x = 316°

$\implies$ x = 79°

Now, we can do the following - substitution of x in the values.

$\longrightarrow$ x = 79°

$\longrightarrow$ x + 15 = 94°

$\longrightarrow$ x + 25 = 104°

$\longrightarrow$ x+ 79 = 83°

Hence, the answers.

Answer 2

Given : Angles of a quadrilateral are x⁰ , (x+15)⁰ , (x+25)⁰ and (x+4)⁰ .

Exigency To Find : The Angles of Quadrilateral.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's Consider $\angle A , \: \angle B \:\angle C \:\& \:\angle D \:$ be the all four angles of Quadrilateral.

$\dag\:\:\it{ As,\:We\:know\:that\::}\\ \bf Angle \: Sum \:Property \:of \: Quadrilateral \:: \:$

⠀⠀⠀⠀⠀━━━ The Sum total of all angles of Quadrilateral is 360⁰ .

$\qquad \dag\:\:\bigg\lgroup \sf{ \angle A + \angle B + \angle C + \angle D = 360^\circ}\bigg\rgroup$

⠀⠀⠀⠀⠀Here ,$\angle A , \: \angle B \:\angle C \:\& \:\angle D \:$ are the four angles of Quadrilateral.

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad :\implies \sf \angle A + \angle B + \angle C + \angle D = 360^\circ$

$\qquad :\implies \sf x + ( x + 15 ) + ( x + 25 ) + ( x + 4) = 360^\circ$

$\qquad :\implies \sf x + x + 15 + x + 25 + x + 4 = 360^\circ$

$\qquad :\implies \sf x + x + x + x +15 + 25 + 4 = 360^\circ$

$\qquad :\implies \sf 4x + 15 + 25 + 4 = 360^\circ$

$\qquad :\implies \sf 4x + 15 + 29 = 360^\circ$

$\qquad :\implies \sf 4x + 44 = 360^\circ$

$\qquad :\implies \sf 4x + 44 = 360 - 44$

$\qquad :\implies \sf 4x = 316$

$\qquad :\implies \sf x = \cancel {\dfrac{316}{4}}$

$\qquad \longmapsto \frak{\underline{\purple{\:x = 79 ^\circ }} }\bigstar$

Therefore,

• First Angle : x = 79⁰
• Second Angle : ( x + 15 ) = 79 + 15 = 94⁰
• Third angle : ( x + 25 ) = 79 + 25 = 104⁰
• Fourth Angle : ( x + 4 ) = 79 + 4 = 83⁰

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \sf \:Four\:angles \:of\:Quadrilateral \:are\:\bf 79 ^\circ , \: 94^\circ ,\:104^\circ \:\:\& \:\:83 ^\circ \: \sf , respectively \:\:.}}$

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