Answer: 39 degrees
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Explanation
The diagonals of a rhombus are always perpendicular.
This leads to triangle ECB being a right triangle. The 90 degree angle at point E.
The other acute angles add to 90
C+B = 90
(5a+4) + (8a-5) = 90
13a-1 = 90
13a = 90+1
13a = 91
a = 91/13
a = 7
This value then leads to:
- angle ECB = 5a+4 = 5*7+4 = 35+4 = 39 degrees
- angle CBE = 8a-5 = 8*7-5 = 56-5 = 51 degrees
Note how 39+51 = 90 to confirm that C+B = 90 is correct. This confirms the correct 'a' value and final answer.
