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

Answer:

y = 5z

Step-by-step explanation:

added in the picture