Question

If the Fore Bearing of the lines AB and BC are 60° and 122°, respectively, then the interior angle \( \angle ABC \) (in degrees) is .......... (round off to the nearest integer).

Hint:

To calculate the interior angle between two lines given their fore bearings, use the formula \( {Interior angle} = ({BB})_{AB} - ({FB})_{BC} \), where the bearing of line AB is adjusted by adding 180° to obtain \( ({BB})_{AB} \).

Answer 1

Given:
- For bearing of line AB, \( ({FB})_{AB} = 60^\circ \)
- For bearing of line BC, \( ({FB})_{BC} = 122^\circ \)
The bearing of line \( ({BB})_{AB} \) is calculated as: \[ ({BB})_{AB} = ({FB})_{AB} + 180^\circ = 60^\circ + 180^\circ = 240^\circ \] The interior angle \( \angle ABC \) is given by: \[ \angle ABC = ({BB})_{AB} - ({FB})_{BC} = 240^\circ - 122^\circ = 118^\circ \] Thus, the interior angle \( \angle ABC \) is \( 118^\circ \).