$A + B + C = 41 + 77 + 63$

$A + B + C = 181^\circ$

$\text{Error} = 181^\circ - 180^\circ$

$\text{Error} = 1^\circ$ ← 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*