If two adjacent angles of a parallelogram are (5x – 5)° and (10x + 35)°, then the ratio of these angles is 1 : 3. Explanation: We know that, adjacent angles of a parallelogram are supplementary, i.e. their sum equals 180°. ∴ (5x – 5) + (10x + 35) = 180° ⇒ 15x + 30° = 180° ⇒ 15x = 150° ⇒ x = 10° Thus, the angles are (5 × 10 - 5) and (10 × 10 + 35), i.e. 45 and 135°. Hence, the required ratio is 45° : 135°, i.e. 1 : 3.
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