Question

The diagonals of a quadrilateral PQRS are equal and meet at O. The opposite sides of the quadrilateral are equal. If Angle SPR =50° . Find...
a. Angle PSO
b. Angle POS
c. Angle QSR​​

Answer 1

Question ⤵

The diagonals of a quadrilateral PQRS are equal and meet at O. The opposite sides of the quadrilateral are equal. If Angle SPR =50° . Find...

1. Angle PSO
2. Angle POS
3. Angle QSR

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Given ⤵

1. The opposite sides of the quadrilateral are equal.
2. ∠SPR =50°
3. Figure in attachment.

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To Find ⤵

1. Angle PSO
2. Angle POS
3. Angle QSR

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$\therefore$ , Diagonal Are Equal.

Opposite Sides are Equal .

$\Rightarrow$PQRS is a Parallelogram.

$\Rightarrow$ Also Diagonal interested at 'O' and Bisect each other.

$\therefore$ PO = OS

$\therefore$ ∠SPO = ∠OSP = 50°

*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*

In △ POS,

50° + 50° + x° = 180° (Sum of angle)

100° + x° = 180°

x° = 180° - 100°

x° = 80°

$\therefore$ ∠SOP = 80° and ∠SPO = 50°

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Answer 2

Answer:

Question ⤵

The diagonals of a quadrilateral PQRS are equal and meet at O. The opposite sides of the quadrilateral are equal. If Angle SPR =50° . Find...

Angle PSO

Angle POS

Angle QSR

____________________________________

Given ⤵

The opposite sides of the quadrilateral are equal.

∠SPR =50°

Figure in attachment.

____________________________________

To Find ⤵

Angle PSO

Angle POS

Angle QSR

____________________________________

$\therefore$ , Diagonal Are Equal.

Opposite Sides are Equal .

$\Rightarrow$PQRS is a Parallelogram.

$\Rightarrow$ Also Diagonal interested at 'O' and Bisect each other.

$\therefore$ PO = OS

$\therefore$ ∠SPO = ∠OSP = 50°

*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*

In △ POS,

50° + 50° + x° = 180° (Sum of angle)

100° + x° = 180°

x° = 180° - 100°

x° = 80°

$\therefore$ ∠SOP = 80° and ∠SPO = 50°

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