Angles 2 and 5 are vertical angles, then they are congruent, that is,
m∠5 = m∠2
m∠5 = 63°
Angles 8 and 9 are supplementary, then their addition is equal to 180°.
m∠8 + m∠9 = 180°
m∠8 + 105° = 180°
m∠8 = 180° - 105°
m∠8 = 75°
Angles 5, 8 and 11 make a triangle. The addition of the angles in a triangle is equal to 180°.
m∠5 + m∠8 + m∠11 = 180°
63° + 75° + m∠11 = 180°
m∠11 = 180° - 63°- 75°
m∠11 = 42°
Angles 12 and 11 are supplementary, then their addition is equal to 180°.
m∠11 + m∠12 = 180°
42° + m∠12 = 180°
m∠12 = 180° - 42°
m∠12 = 138°
