Answer:
m∠1 = 120°
m∠3 = 30°
m∠2 = 30°
Step-by-step explanation:
Properties of a rhombus,
1). Diagonals bisect the opposite angles in a rhombus.
2). Opposite angles of a rhombus are equal in measure.
3). Sum of adjacent two angles of a rhombus equals to 180°.
By property (2),
m∠1 = 120°
By property (3),
m∠B + m∠C = 180°
m∠C = 180° - 120°
m∠C = 60°
By property (1),
m∠ACB = m∠ACD = [tex]\frac{60}{2}[/tex]
m∠3 = 30°
m∠A = m∠C = 60°
m∠2 = [tex]\frac{m\angle BAD}{2}[/tex]
= 30°
