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Question
The sum of two opposite angles of a parallelogram is 130°. Find all the angles of the parallelogram.
Solution
\[\text{ Let the angles be A, B, C and D }. \]
\[\text{ It is given that the sum of two opposite angles is } 130°. \]
\[ \therefore \angle A + \angle C = 130°\]
\[\angle A + \angle A = 130° \left( \text{ opposite angles of a parallelogram are same } \right)\]
\[\angle A = 65°\]
\[\text{ and } \angle C = 65°\]
\[\text{ The sum of adjacent angles of a paralle\logram is } 180° . \]
\[\angle A + \angle B = 180°\]
\[65°+ \angle B = 180°\]
\[\angle B = 180°- 65°\]
\[\angle B = 115°\]
\[ \angle D = 115°\]
\[ \therefore \angle A = 65°, v\angle B = 115°, \angle C = 65° \text{ and } \angle D = 115° .\]
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