Question

100 pts!!

Let Θ = 60°42'. Find the measure of the supplement of Θ.

Equation: Θ = 180° - 60°42'


(I already know the equation for this but I was wondering if someone can give me a step by step guide on how to do the math on paper?)

Answer 1

• 119°18'

Given :

• Θ = 60°42'

To find :

• Supplement of 60°42'

Solution :

We know that,

• Supplement of an angle + Angle = 180°
• Supplement of 60°42' + 60°42' = 180°
• Supplement of 60°42' = 180° - 60°42'

We can convert 60°42' into degrees by dividing 42 minutes by an hour i.e.

• 60° + (42/60)° = 60° + 0.7° = 60.7°

Thus,

• Supplement of 60°42' = 180° - 60.7°
• Supplement of 60°42' = 119.3°
• Supplement of 60°42' = 119° + (3x60)' = 119°18'

Thus, 119°18' would be the required answer.

Answer 2

θ' = 119°18'

Explanation:

Degrees (°), minutes ('), and seconds (") are units used to precisely measure angles, with degrees being the largest unit, minutes subdividing degrees, and seconds providing the finest level of angular detail.

The given angle θ is 60°42', which translates to 60 degrees and 42 minutes.

The supplement of an angle is an angle that, when added to the given angle, results in a sum of 180°. Therefore, to find the supplement (θ'), we can subtract θ = 60°42' from 180°.

θ' = 180° - 60°42'

Since angle θ is in Degrees-Minutes-Seconds format, we express 180° in the same format:

θ' = 180°0'0" - 60°42'0"

Being by subtracting the seconds. As both are zero, this results in 0 seconds.

θ' = 180°0'0" - 60°42'0"

Next, subtract the minutes. Since 0 - 42 would be negative, borrow 1 degree (60 minutes) from the degrees component of the first angle and add it to the minutes of the first angle:

θ' = 179°60'0" - 60°42'0"

Subtract the minutes to get:

θ' = 179°18'0" - 60°0'0"

Finally, subtract the degrees of the second angle from the degrees of the first angle:

θ' = 119°18'0"

As there are zero seconds, we can rewrite this as:

θ' = 119°18'