Angle Measurement

Angles are measured in degrees or radians. A complete circle has 360 or 2π radians. Therefore 360 = 2π radians.
Divide both sides by two and you have  1800 = π radians.

Therefore if we divide both sides by 180 we will find what 1 equals in radians.
1800∕ 180 = π radians ∕ 180 → 10 = π radians ∕ 180 → 10 ≈ 0.01745329 radians.
( The above problem isn't any more difficult than 3t = 12
t would represent the degree symbol 0   3t/3 = 12/3  → 1t = 12/3  →  1t = 4
)

Hence to change 15 to radians multiply both sides by 15 × 10 = 15 × π radians ∕ 180 → π radians ∕ 12
π radians divided by 12 and we get 150 ≈ .2617883878 radians. If we used (10 ≈ 0.01745329 radians) × 15 ≈ .26179935.
We get a slightly different answer.

Due to rounding off the numbers involved in the calculations both answers are approximations.

However π radians ∕ 180  multiplied by 15 is a more accurate answer. Hence we used the latter instead of 0.01745329

What does 160answer

Our next consideration is that each degree equals 60 minutes and each minute equals 60 seconds.
So you can have a degree measurement of  13015' 11"

How do you change 13015' 11" to radian measure? answer

Using the information that  1800 = π radians can you explain how to change
from radians to degrees?   Hint 5 radians ≈ 286.478898o answer

What are: acute angles, obtuse angles, complementary angles, supplementary angles, straight angles
and right angles? answer

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