Question

If a || b, m<2=63°, and m<9=105°, find the missing measure of m<14=?

Answer 1

m∠14 = 138°

Explanation:

∠2 = ∠5 = 63° (vertically opposite angles)

∠9 +∠8 = 180° (linear pair)
=> 105° + ∠8 = 180
=> ∠8 = 180° - 105° = 75°

∠5 + ∠8 + ∠11 = 180° (sum of angles in a triangle is 180)
=> 63° + 75° + ∠11 = 180°
=> 138° + ∠11 = 180°
=> ∠11 = 180° - 138° = 42°

∠11 + ∠14 = 180° (linear pair)
=> 42° + ∠14 = 180°
=> ∠14 = 180° - 42° = 138°

Hope you understood!!