According to the Triangle Angle-Sum Theorem the measures of the interior angles of a triangle add to 180^(∘). Note that one of the angles is a right angle, so the triangle is a right triangle. This means that the acute angles are complementary. In this case, (4x-2)^(∘) and (3x+8)^(∘) add to 90^(∘).
(4x-2)+(3x+8)=90
By solving this equation, we can find the value of x.
We found that x=12. Let's substitute this value to the expressions of the acute angles to find their measures.
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(4x-2)^(∘) &→ & (4( 12)-2)^(∘) &→ & 46^(∘)
(3x+8)^(∘) &→ & (3( 12)+8)^(∘) &→ & 44^(∘)
Therefore, the measures of the acute angles are 44^(∘) and 46^(∘).
