Question

In the givem figure, if HOPE is rhombus, then find anglePEO and anglePEO​

Answer 1

$\huge\sf\pink{Answer}$

☞ ∠PEO & ∠POE are equal to 70°

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$\huge\sf\blue{Given}$

✭ ∠OPE = 30°

✭ HOPE is a Rhombus

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$\huge\sf\gray{To \:Find}$

◈ ∠PEO & ∠POE

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$\huge\sf\purple{Steps}$

$\large\underline{\underline{\textsf{Correct Question}}}$

In the givem figure, if HOPE is rhombus, then find ∠PEO and ∠POE

$\large\underline{\underline{\textsf{Concept}}}$

»» In a Rhombus diagonals bisect in right angles (90°)

»» Angles opposite to equal sides are equal

»» In a triangle angles add up to 180°

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In ∆PQE

◕ ∠QPE = 30° «« Given »»

◕ ∠POE = 90° «« Diagonals bisect in 90° »»

◕ ∠PEO = ?

We know that in a triangle,

➝ $\sf \angle OPE + \angle POE + \angle PEO = 180^{\circ}$

➝ $\sf 30^{\circ} + 90^{\circ} + \angle PEO = 180^{\circ}$

➝ $\sf 110^{\circ} + \angle PEO = 180^{\circ}$

➝ $\sf \angle PEO = 180-110$

➝ $\sf \red{\angle PEO = 70^{\circ}}$

Now in ∆PEO

➳ $\sf PE = PO$ «« All sides of a Rhombus are equal »»

➳ $\sf \angle PEO = \angle POE$ «« Angles opposite to equal sides »»

➳ $\sf \orange{\angle POE = 70^{\circ}}$

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