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Question
If two adjacent angles of a parallelogram are (5x – 5)° and (10x + 35)°, then the ratio of these angles is ______.
Options
1 : 3
2 : 3
1 : 4
1 : 2
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Solution
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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