# Angles

Determine the interior angles of a rhombus with area 319.1 cm2 and perimeter 72 cm.

Result

α =  80 °
β =  100 °
γ =  80 °
δ =  100 °

#### Solution:

$a = 72 / 4 = 18 \ cm \ \\ S = a^2 \sin \alpha \ \\ \ \\ \alpha = arcsin( \dfrac{ 319.1 }{ 18 ^2 } ) = 80 ^\circ$
$\beta = 180 ^\circ - \alpha = 100 ^\circ$
$\gamma = \alpha = 80 ^\circ$
$\delta = \beta = 100 ^\circ$

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