To solve for the measure of angle $B$ in a triangle, we can use the fact that the sum of the interior angles of any triangle is always 180 degrees.

Given the following angles:

• $A = 32^\circ 48'$
• $C = 27^\circ 32'$

We can calculate $B$ as follows:

$B = 180^\circ - A - C$ $B = 180^\circ - (32^\circ 48') - (27^\circ 32')$

To make the calculation easier, let's break it down:

1. First, subtract the degrees: $180^\circ - 32^\circ - 27^\circ = 121^\circ$

2. Then, subtract the minutes: $0' - 48' - 32' = -80'$

Since we have a negative result for the minutes, we need to adjust the degrees by borrowing 1 degree (which is 60 minutes):

$121^\circ - 1^\circ = 120^\circ$ $60' - 80' = -20'$

Therefore, the measure of angle $B$ is: $B = 120^\circ - 20' = 119^\circ 40'$

So, the measure of angle $B$ is approximately: $B = 119^\circ 40'$

Would you like further details on the steps, or do you have any questions?

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Here are 5 related questions you might find helpful:

1. How do you convert degrees and minutes into decimal degrees?
2. What is the sum of the interior angles of a polygon with more than three sides?
3. How do you handle cases when the angles include seconds (e.g., $48"$)?
4. How do you find the third angle of a triangle given the other two angles and one side?
5. What is the sine rule, and when is it applied in triangle problems?

Tip: Always remember that $1^\circ = 60'$ and $1' = 60"$ when working with degrees, minutes, and seconds.