Question

The opposite angle of a quadrilateral is supplementary to each other. If the difference between the pairs of opposite angles is 40° and 50°, Find the measure of the angles of the quadrilateral ​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• Opposite angles of a quadrilateral is supplementary.
• Difference between pairs of opposite angles is 40° & 20°

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$\red{\underline \bold{To \: Find:}}$

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• Measure of angles of the quadrilateral

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let one one pair of opposite angle be x & y

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So,

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⇛ x + y = 180° --------(1)

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⇛ x - y = 40° -----------(2)

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$\underline{\bold{\texttt{Solving (1) \& (2) we get,}}}$

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⇛ 2x = 220

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⇛ x = 110°

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Hence,

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⇛ y = 70°

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Let other pair of opposite angles be a & b

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So,

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⇛ a + b = 180° ----------(3)

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⇛ a - b = 50° -----------(4)

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$\underline{\bold{\texttt{Solving (3) \& (4) we get,}}}$

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⇛ 2a = 230

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⇛ a = 115°

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Hence,

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⇛ b = 65°

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$\underline{\bold{\texttt{Hence angles are :}}}$

• 110°
• 70°
• 115°
• 65°

$\rule{200}5$

Answer 2

Step-by-step explanation:

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