$A + B + C = 41 + 77 + 63$
$A + B + C = 181^\circ$
$\text{Error} = 181^\circ - 180^\circ$
$\text{Error} = 1^\circ$ ← An excess of 1° in sum, hence, subtract the correction
Angles with more number of measurements will receive less error correction.
Weight of Error for Angle A = 1/2
Weight of Error for Angle B = 1/6
Weight of Error for Angle C = 1/2
| Vertex |
Angle |
Weight |
Correction |
Corrected Angle |
| A |
41° |
1/2 |
$1^\circ \times \dfrac{1/2}{7/6} = \dfrac{3^\circ}{7}$ |
40.517° |
| B |
77° |
1/6 |
$1^\circ \times \dfrac{1/6}{7/6} = \dfrac{1^\circ}{7}$ |
76.857° |
| C |
63° |
1/2 |
$1^\circ \times \dfrac{1/2}{7/6} = \dfrac{3^\circ}{7}$ |
62.571° |
| SUM |
181° |
7/6 |
1° |
180° |
Most probable value of angle C = 62.571° ← answer
