# ABCD is a rhombus.If angle ADB = 50, find all the angles of the rhombus?

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Dec 11, 2016

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#### Explanation:

A Rhombus has the following properties :

1) The sides of a rhombus are all congruent (the same length.)
$\implies A B = B C = C D = D A$

2) $A C \mathmr{and} B D$ are perpendicular.

3) $A O = O C , \mathmr{and} B O = O D$

4) $\Delta A O B , \Delta C O B , \Delta C O D \mathmr{and} \Delta A O D$ are congruent

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Now back to our question,

Given that $\angle A D B = {50}^{\circ} = \angle A D O$,

$\angle O A D = 90 - 50 = {40}^{\circ}$

$\implies \angle O B A = \angle O B C = \angle O D C = O D A = {50}^{\circ}$
$\implies \angle O A B = \angle O C B = \angle O C D = \angle O A D = {40}^{\circ}$

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