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Question
Two opposite angles of a parallelogram are (3x − 2)° and (50 − x)°. Find the measure of each angle of the parallelogram.
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Solution
\[\text{ Oppostie angles of a parallelogram are congurent } . \]
\[ \therefore \left( 3x - 2 \right)° = \left( 50 - x \right)°\]
\[3x°- 2° = 50°- x°\]
\[3x°+ x°= 50° + 2°\]
\[4x°= 52°\]
\[x° = 13°\]
\[\text{ Putting the value of x in one angle }: \]
\[3x° - 2°= 39°- 2°\]
\[ = 37°\]
\[\text{ Opposite angles are congurent }: \]
\[ \therefore 50 - x°\]
\[ = 37°\]
\[\text{ Let the remaining two angles be y and z } . \]
\[\text{ Angles y and z are congurent because they are also opposite angles } . \]
\[ \therefore y = z\]
\[\text{ The sum of adjacent angles of a paralle\logram is equal to } 180° . \]
\[ \therefore 37°+ y = 180°\]
\[y = 180°- 37°\]
\[y = 143°\]
\[\text{ So, the anlges measure are }: \]
\[37°, 37°, 143° \text{ and } 143°\]
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