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What is angle ecb? (rhombus)

What is angle ecb? (rhombus)-example-1
User MikeBeaton
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1 Answer

7 votes

Answer: 39 degrees

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Step-by-step 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.

User Roland Ewald
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4.3k points