Angles of a Rhombus

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.

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.

The interior angles of a rhombus
are bisected by the diagonals.

Example

Find the measure of angle ABC and the measure of angle PAB. The measure of angle ADP: 50 degrees.

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.