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Question
Two adjacent angles of a parallelogram are (3x − 4)° and (3x + 10)°. Find the angles of the parallelogram.
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Solution
\[\text{ We know that the adjacent angles of a parallelogram are supplementry } . \]
\[\text{ Hence }, \left( 3x + 10 \right)° \text{ and } \left( 3x - 4 \right)° \text{ are supplementry } . \]
\[\left( 3x + 10 \right)°+ \left( 3x - 4 \right)° = 180°\]
\[6x° + 6°= 180°\]
\[6x° = 174°\]
\[x = 29°\]
\[\text{ First angle } = \left( 3x + 10 \right)°= \left( 3 \times 29° + 10° \right) = 97°\]
\[\text{ Second angle }= \left( 3x - 4 \right)° = 83°\]
\[\text{ Thus, the angles of the parallelogram are } 97°, 83°, 97° \text{ and } 83°.\]
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