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Question
The adjacent angles of a parallelogram are (2x – 4)° and (3x – 1)°. Find the measures of all angles of the parallelogram.
Solution
Since, the adjacent angles of a parallelogram are supplementary.
We know that the adjacent angles of a parallelogram are supplementary. So,
(2x – 4)° + (3x – 1)° = 180°
5x – 5° = 180°
5x = 185°
x = `185^circ/5`
x = 37°
So, 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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