Question

This is a rhombus. Using its properties, what is the measure of:

Angle 1: ___ degrees

Angle 2: ___ degrees

Angle 3: ___ degrees

Answer 1

m∠1 = 120°

m∠3 = 30°

m∠2 = 30°

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 =
`(60)/(2)`

m∠3 = 30°

m∠A = m∠C = 60°

m∠2 =
`(m\angle BAD)/(2)`

= 30°