The diagonals of a quadrilateral PQRS are equal and meet at O. The opp

1.	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 PSOb. Angle POS c. Angle QSR
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° ____________________________________

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 PSOb. Angle POS c. Angle QSR

Answer»

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...

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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°

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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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