Question
The adjacent angles of a parallelogram are (2x−4)∘ and (3x−1)∘. Find the measures of all angles of the parallelogram.
The adjacent angles of a parallelogram are (2x−4)∘ and (3x−1)∘. Find the measures of all angles of the parallelogram.
Answer:
:
The adjacent angles of a parallelogram are supplementary.
∴(2x−4)∘+(3x−1)∘=180∘
⇒5x−5∘=180∘⇒5x=185∘⇒x=185∘5⇒x=37∘
Thus, the adjacent angles are
2x−4=2×37∘−4=74−4=70∘.
and 3x−1=3×37∘−1=111−1=110∘
Hence, the angles are 70∘,110∘,70∘,110∘.
[∵ Opposite angles in a parallelogram are equal].
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:
The adjacent angles of a parallelogram are supplementary.
∴(2x−4)∘+(3x−1)∘=180∘
⇒5x−5∘=180∘⇒5x=185∘⇒x=185∘5⇒x=37∘
Thus, the adjacent angles are
2x−4=2×37∘−4=74−4=70∘.
and 3x−1=3×37∘−1=111−1=110∘
Hence, the angles are 70∘,110∘,70∘,110∘.
[∵ Opposite angles in a parallelogram are equal].
Was this answer helpful ?
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