Questions: 286° 32,6' + 180° - 189° 37,6' =

Solution Steps

To solve this problem, we need to perform arithmetic operations on angles given in degrees and minutes. First, convert all angles to a consistent format (either all in degrees or all in minutes). Then, perform the addition and subtraction operations. Finally, convert the result back to degrees and minutes if necessary.

We start by converting each angle to total minutes:

• For \( 286^{\circ} 32.6^{\prime} \): \[ 286^{\circ} 32.6^{\prime} = 286 \times 60 + 32.6 = 17192.6 \text{ minutes} \]
• For \( 180^{\circ} \): \[ 180^{\circ} = 180 \times 60 + 0 = 10800 \text{ minutes} \]
• For \( 189^{\circ} 37.6^{\prime} \): \[ 189^{\circ} 37.6^{\prime} = 189 \times 60 + 37.6 = 11377.6 \text{ minutes} \]

Next, we perform the operation: \[ 17192.6 + 10800 - 11377.6 \] Calculating this gives: \[ 17192.6 + 10800 = 27992.6 \] \[ 27992.6 - 11377.6 = 16615.0 \text{ minutes} \]

Now, we convert \( 16615.0 \) minutes back to degrees and minutes:

• Degrees: \[ \text{Degrees} = \left\lfloor \frac{16615.0}{60} \right\rfloor = 276 \]
• Minutes: \[ \text{Minutes} = 16615.0 \mod 60 = 55.0 \]

Final Answer