If the length of one side of a rhombus is equal to the length of one diagonal, find the angles of the rhombus.

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Solution

$O n e o f t h e d i a g o n a l s o f a r h o m b u s i s e q u a l t o o n e o f i t s s i d e s .$

$W e k n o w t h a t a r h o m b u s h a s f o u r e q u a l s i d e s . I f o n e s i d e h a s t h e s a m e l e n g t h a s a d i a g o n a l, t h e d i a g o n a l i s p a r t o f t w o e q u i l a t e r a l t r i a n g l e s . S i n c e a r h o m b u s h a s f o u r s i d e s w e c a n s a y$

$R h o m b u s = A B C D, w h e r e A B = d i a g o n a l o f A C, S i n c e t h e t r i a n g l e A B C i s e q u i l a t e r a l a n d s o a n g l e A B C = 60. T o s o l v e t h e p r o b l e m w e c a n m a k e a n e q u a t i o n .$

$60 + x = 180$

$S o l v i n g 60 + x = 180$

$180 - 60 = x$

$x = 120$

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