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