# Angles of a Rhombus

How to solve the angles of a rhombus problems: properties, example, and its solution.

## Properties

The opposite interior angles of a rhombus are congruent.

(= Same colored angles are congruent.)

The interior angles of a rhombus

are bisected by the diagonals.

## Example

*DB* bisects ∠*ADC*.

Then m∠*ADB* = m∠*BDC = 50.*

And m∠*ADC* = 50 + 50 = 100.

∠*ADC* and ∠*ABC* are opposite angles,

which are congruent.

So m∠*ADC* = m∠*ABC* = 100.

△*ADP* is a right triangle.

Then m∠(purple dot) + m∠(blue dot, 50) + 90 = 180.

m∠(purple dot) + 50 = 90

m∠(purple dot) = 40 (= m∠*DAP*)*AC* bisects ∠*DAB*.

Then m∠*DAP* = m∠*PAB* = 40.