Find $ \angle EBC $ from the following figure.
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Given :

The given figure is a rhombus.

$\angle EBC = (8a - 5)° , \angle ECB = (5a + 4)° $

To find :

We have to the $\angle EBC$

Solution :
 

The given figure is a Rhombus, In rhombus diagonals are perpendicular to each other.

So, $\angle BEC = 90°$

 Sum of all angles of triangle = 180°.

In $\Delta BEC$,

$\angle BEC + \angle EBC + \angle ECB = 180° $

$90° + (8a - 5)° + (5a + 4)° = 180°$

$90° + 8a + 5a -5 + 4 = 180°$

$90° - 1 + 13 a = 180°$

$89 + 13 a = 180°$

$13 a = 180 - 89$

$13 a = 91$

$a = \frac{91}{13}$

$a = 7$

Substitute the value of a in $\angle EBC = (8a - 5)°$

$\angle EBC = (8 \times 7 - 5)°$

$\angle EBC = (56 - 5)°$

$\angle EBC = 51°$

Therefore, $\angle EBC$ is $51°$

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Updated on: 10-Oct-2022

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