Question

Find y in terms with z. help me please :)​

Answer 1

`\quad \huge \quad \quad \boxed{ \tt \:Answer }`

• 
  `\qquad \tt \rightarrow y = 5z`

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`\large \tt Solution \: :`

[ let the point at which line segments SV and RT intersects be O ]

`\qquad \tt \rightarrow \: \angle ROV + \angle ROS = 180°`

[ linear pair ]

`\qquad \tt \rightarrow \: \angle ROV = 180 - \angle ROS`

`\qquad \tt \rightarrow \: \angle ROV = 180 -2y`

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`\qquad \tt \rightarrow \: \angle SVU = \angle ROV + \angle TRV`

[ Exterior angle = sum of opposite interior angles ]

`\qquad \tt \rightarrow \: \angle SVU = 180 - 2y + y`

`\qquad \tt \rightarrow \: \angle SVU = 180 - y`

( let it be equation 1 )

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`\qquad \tt \rightarrow \: \angle SVU + \angle SUV + \angle VSU = 180°`

[ Sum of angles of Triangle ]

`\qquad \tt \rightarrow \: \angle SVU + 4z + z = 180°`

`\qquad \tt \rightarrow \: \angle SVU + 5z = 180°`

`\qquad \tt \rightarrow \: \angle SVU = 180° - 5z`

( let it be equation 2 )

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By comparing both equations :

`\qquad \tt \rightarrow \: \angle SVU = 180 - y = 180 - 5z`

`\qquad \tt \rightarrow \: 180 - y = 180 - 5z`

( Add 180° on both sides )

`\qquad \tt \rightarrow \: 180 - y + 180 = 180 - 5z + 180`

`\qquad \tt \rightarrow \: - y = - 5z`

`\qquad \tt \rightarrow \: y = 5z`

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer 2

y = 5z

Explanation:

added in the picture