What is the value of M

1. 34 degrees

2. 56 degrees

3. 90 degrees

4. 180 degrees

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°.