Two adjacent angles of a parallelogram are in the ratio 1:1 find the measures of all the angles

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\[\text{ Let the angle be A and B }. \]\[\text{ The angles are in the ratio of 1: 2 } . \]\[\text{ Measures of } \angle A \text{ and } \angle B \text{ are } x°  \text{ and } 2x° . \]\[Then, \angle C = \angle A and \angle D = \angle B (\text{ opposite angles of a parallelogram are congruent })\]\[\text{ As we know that the sum of adjacent angles of a parallelogram is } 180°. \]\[ \therefore \angle A + \angle B = 180°\]\[ \Rightarrow x° + 2x°= 180°\]\[ \Rightarrow 3x° = 180°\]\[ \Rightarrow x°= \frac{180°}{3} = 60°\]

\[\text{ Thus, measure of } \angle A = 60°, \angle B = 120°, \angle C = 60° \text{ and } \angle D = 120° .\]