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Question
Two adjacent angles of a parallelogram are as 1 : 2. Find the measures of all the angles of the parallelogram.
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Solution
\[\text{ Let the angle be A and B }. \]
\[\text{ The angles are in the ratio of 1: 2 } . \]
\[\text{ Measures of } \angle A \text{ and } \angle B \text{ are } x° \text{ and } 2x° . \]
\[Then, \angle C = \angle A and \angle D = \angle B (\text{ opposite angles of a parallelogram are congruent })\]
\[\text{ As we know that the sum of adjacent angles of a parallelogram is } 180°. \]
\[ \therefore \angle A + \angle B = 180°\]
\[ \Rightarrow x° + 2x°= 180°\]
\[ \Rightarrow 3x° = 180°\]
\[ \Rightarrow x°= \frac{180°}{3} = 60°\]
\[\text{ Thus, measure of } \angle A = 60°, \angle B = 120°, \angle C = 60° \text{ and } \angle D = 120° .\]
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