Question

The adjacent figure HOPE is a parallelogram. Find the angle measures , . State the properties you use to find them



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Answer 1

$\large\underline{\sf{Solution-}}$

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°

⇛ z = 70° - 40° = 30°.

Now, OH || FE & HE is transversal.

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

$\rm \implies\:z + 40\degree + x = 180 \degree$

$\rm \implies\:30\degree + 40\degree + x = 180 \degree$

$\rm \implies\:70\degree + x = 180 \degree$

$\rm \implies\:x = 180 \degree - 70\degree$

$\rm \implies\:x = 110 \degree$

Thus,

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{x = 110\degree} \\ \\ &\sf{y = 40\degree} \\ \\ &\sf{z = 30\degree} \end{cases}\end{gathered}\end{gathered}$

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More to know,

1. Diagonals of a parallelogram bisects each other.

2. Opposite angles of parallelogram are equal.

3. Opposite Sides are equal.

4. Opposite Sides are parallel.

5. Sum of Adjacent angles are supplementary.

Answer 2

x=110

y=40

z=30

Step-by-step explanation:

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