m∠a = 56°, m∠b = 34°, m∠c = 56°
Solution:
Sum of the adjacent angles in a straight line is 180°.
⇒ m∠a + 124° = 180°
⇒ m∠a = 180° – 124°
⇒ m∠a = 56°
∠a and ∠c are vertically opposite angles.
Vertical angle theorem:
If two lines are intersecting, then the vertically opposite angles are congruent.
⇒ ∠a ≅ ∠c
⇒ m∠a = m∠c
⇒ m∠c = 56°
Sum of the adjacent angles in a straight line is 180°.
m∠b + 90° + m∠c = 180°
m∠b + 90° + 56° = 180°
m∠b + 146° = 180°
m∠b = 180° – 146°
m∠b = 34°
Hence m∠a = 56°, m∠b = 34°, m∠c = 56°.
