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If the given figure find the value of x, y and z.

I m giving you thirty pts please give me correct answer.​

If The Given Figure Find The Value Of X Y And ZI M Giving You Thirty Pts Please Give Me Correct Answer class=

Sagot :

SalmonWorldTopperidn

[tex]\large\underline{\sf{Explanation-}}[/tex]

Given that

HOPE is a parallelogram.

It means,

  • OH || FE and HE || PO

Now, HE || PO & HP is transversal.

  • So, "y" = 40 ° [ alternate interior angles ]

Now, In triangle HOP

We know, Exterior angle of a triangle is equals to sum of interior opposite angles.

  • So, y + z = 70°

It means, 40° + z = 70°

[tex]\longmapsto[/tex]"z" = 70° - 40° = 30°.

Now, OH || FE & HE is transversal.

So, we know, sum of Adjacent angles of a parallelogram is supplementary.

[tex]\rm \longmapsto\:z + 40\degree + x = 180 \degree[/tex]

[tex]\rm \longmapsto\:30\degree + 40\degree + x = 180 \degree[/tex]

[tex]\rm \longmapsto\:70\degree + x = 180 \degree[/tex]

[tex]\rm \longmapsto\:x = 180 \degree - 70\degree[/tex]

[tex]\longmapsto\:\bf{"x"} = 110 \degree [/tex]

Therefore, the measure of the following angle are:

  • x = 110°
  • y = 40° and
  • z = 30°
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