The sum of two opposite angles of a parallelogram is 130°. Find all the angles of the parallelogram.

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#### 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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