2. The ratio of the measures of the supplementary angle to the complementary
angle of a given angle is 8:3. What will be the ratio of the angle to its
supplementary angle?
(2) 1:3 (3) 1:4
(1) 4:1
(4) 1:2
please give step by step explanation
Answers
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Given:
- Angle in ratio = 8 : 3
To Find:
- Supplementary angle.
Solution:
☯ Let the angle be "x".
- Supplementary angle = 180 - x
- Complementary angke = 90 - x
According to the given condition,
→ 180 - x / 90 - x = 8 / 3
Cross multiply
→ 3(180 - x) = 8(90 - x)
→ 540 - 3x = 720 - 8x
→ 5x = 720 - 540
→ 5x = 180
Divide both the sides by 5
→ x = 36
The measure of the angle is 36°
★ Supplementary angle ➾ 180 - x
→ 180 - 36
→ 144°
Ratio of the angle to its supplementary angle
→ 36 / 144 [Divide by 36]
→ 1 / 4
→ 1 : 4
Hence,
- Ratio of its supplementary angle = 1 : 4
- Therefore, option (3) is correct.
Anonymous:
Wonderful❣
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