The acute angles in the triangle are 16.6 degrees and 73.4 degrees
From the question, we have:
Triangle type = Right triangle
Let the acute angles be x and y.
So, we have:
3/4x = 1/4 + 1/6y
Multiply through by 12
9x = 3+ 2y
The sum of acute angles in a right triangle is
x + y = 90
Rewrite as
y = 90 - x
Substitute y = 90 - x in 9x = 3+ 2y
9x = 3+ 2(90 - x)
Open the brackets
9x = 3+ 180 - 2x
Evaluate the like terms
11x = 183
Divide by 11
x = 183/11 = 16.6
Substitute x = 183/11 in y = 90 - x
y = 90 - 183/11
Evaluate
y = 807/11 = 73.4
Hence, the acute angles in the triangle are 16.6 degrees and 73.4 degrees
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