# Angle Correction for Repeated Measurement

**Problem**

The following interior angles (in degree) of a triangular traverse were measured with the same precision.

Angle | Value | No. of Measurement |
---|---|---|

A |
41 | 2 |

B |
77 | 6 |

C |
63 | 2 |

What is the most probable value of angle *C*, in degrees?

A. 62.423° | C. 62.571° |

B. 62.874° | D. 62.745° |

**Answer Key**

[ C ]

**Solution**

$A + B + C = 41 + 77 + 63$
Weight of Error for Angle

Weight of Error for Angle

Weight of Error for Angle

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

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

$\text{Error} = 1^\circ$ ← An excess of 1° in sum, hence, subtract the correction

Angles with more number of measurements will receive less error correction.

*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*

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