The opposite angles of quadrilateral are supplementary to each other. If the difference between the pair of opposite angles is 40° and 20°, Find the measure of the angles of the quadrilateral.
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The opposite angles of quadrilateral are supplementary to each other. If the difference between the pair of opposite angles is 40° and 20°, Find the measure of the angles of the quadrilateral.
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Answer:
Answer:
Given:
Opposite angles of a quadrilateral is supplementary.
Difference between pairs of opposite angles is 40° & 20°
ToFind:
Measure of angles of the quadrilateral
Solution:−
\:\:
Let one one pair of opposite angle be x & y
\:\:
So,
\:\:
⇛ x + y = 180° --------(1)
\:\:
⇛ x - y = 40° -----------(2)
\:\:
\underline{\bold{\texttt{Solving (1) \& (2) we get,}}}
Solving (1) & (2) we get,
\:\:
⇛ 2x = 220
\:\:
⇛ x = 110°
\:\:
Hence,
\:\:
⇛ y = 70°
\:\:
Let other pair of opposite angles be a & b
\:\:
So,
\:\:
⇛ a + b = 180° ----------(3)
\:\:
⇛ a - b = 20° -----------(4)
\:\:
\underline{\bold{\texttt{Solving (3) \& (4) we get,}}}
Solving (3) & (4) we get,
\:\:
⇛ 2a = 200
\:\:
⇛ a = 100°
\:\:
Hence,
\:\:
⇛ b = 80°
\:\:
\underline{\bold{\texttt{Hence angles are :}}}
Hence angles are :
110°
70°
100°
80°
\rule{200}5
Answer:
x=110 and y=70
Step-by-step explanation:
and other angles opposite angles