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Complementary and supplementary angles of

4π/9are:
a) Complementary: 5π/9, Supplementary: 14π/9
b) Complementary: 5π/9, Supplementary: 5π/9
c) Complementary: 9π/4, Supplementary: 5π/8
d) Complementary: 5π/9, Supplementary: 9π/4

User Buren
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1 Answer

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Final answer:

The correct complementary and supplementary angles for 4π/9 radians are 5π/9 and 10π/9 radians, respectively. The provided options were incorrect; the corrected values are derived from the complementary addition to π/2 and the supplementary addition to π. Option (b) Complementary: 5π/9, Supplementary: 5π/9 radians, is the correct answer

Step-by-step explanation:

To solve the question about complementary and supplementary angles to a given angle of 4π/9 radians, we will recall two key concepts:

  • Complementary angles are two angles whose measures add up to π/2 radians (which is 90°).
  • Supplementary angles are two angles whose measures add up to π radians (which is 180°).

Given the angle 4π/9 radians, let's find its complementary and supplementary angles.

We subtract the given angle from π/2:

π/2 - 4π/9 = (9π/18 - 8π/18) = π/18

Therefore, the complementary angle is π/18 radians, which simplifies to 5π/9 radians.

We subtract the given angle from π:

π - 4π/9 = (9π/9 - 4π/9) = 5π/9

Therefore, the supplementary angle is also 5π/9 radians.

As we can see, there was an error in the computations above; complementary and supplementary angles should be distinct, and it seems unlikely they would be equal. Let's correct this:

π/2 - 4π/9 = (9π/18 - 8π/18) = 5π/18

When simplified, the correct complementary angle is 5π/18 radians, which is equivalent to 5π/9 radians.

π - 4π/9 = (9π/9 - 4π/9) = 5π/9

When simplified, the correct supplementary angle is 5π/9 radians, which is equivalent to 10π/9 radians.

Thus, option (b) Complementary: 5π/9, Supplementary: 5π/9 radians, is the correct answer, as it results from the correct calculations.

User Xangr
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