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प्रश्न
Two opposite angles of the parallelogram are 3x – 5° and x + 45°. Find the angles of the parallelogram.
योग
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उत्तर
Given: Two opposite angles of the parallelogram are 3x – 5° and x + 45°.
Step-wise calculation:
1. Opposite angles in a parallelogram are equal and adjacent angles are supplementary.
2. Set the opposite angles equal:
3x – 5 = x + 45
3. Solve:
3x – x = 45 + 5
⇒ 2x = 50
⇒ x = 25
4. Evaluate the angles:
3x – 5 = 3(25) – 5
= 75 – 5
= 70°
Also x + 45
= 25 + 45
= 70°
5. Adjacent angles
= 180° – 70°
= 110°
The angles of the parallelogram are 70°, 110°, 70°, 110°.
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