Question

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

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

Answer 1

`\large\underline{\sf{Explanation-}}`

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°

`\longmapsto`"z" = 70° - 40° = 30°.

Now, OH || FE & HE is transversal.

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

`\rm \longmapsto\:z + 40\degree + x = 180 \degree`

`\rm \longmapsto\:30\degree + 40\degree + x = 180 \degree`

`\rm \longmapsto\:70\degree + x = 180 \degree`

`\rm \longmapsto\:x = 180 \degree - 70\degree`

`\longmapsto\:\bf{`

Therefore, the measure of the following angle are:

• x = 110°
• y = 40° and
• z = 30°