Chapter Review
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Consider the Triangle Angle-Sum Theorem.
35^(∘), 55^(∘)
Let's analyze the given triangle.
According to the Triangle Angle-Sum Theorem the measures of the interior angles of a triangle add to 180^(∘). Since one of the angles is a right angle, the acute angles are complementary. In this case, it means that (7x+6) and (6x-7) add to 90.
Add and subtract terms
LHS+1=RHS+1
.LHS /13.=.RHS /13.
Once we know the value of x, we can find the measures of acute angles. ccc (7x+6)^(∘) &→& (7( 7)+6)^(∘)&→& 55^(∘) (6x-7)^(∘) &→& (6( 7)-7)^(∘)&→& 35^(∘) Therefore, the measures of the acute angles are 35^(∘) and 55^(∘).