Exercise 4 Page 591

Let's analyze the given triangle.

As we can see, one of its angles is a right angle, and therefore it is a right triangle. This allows us to use Triangle Angle-Sum Theorem, which states that acute angles of a right triangle are complementary. In this case, it means that 2x and (x-6) add up to 90. 2x+(x-6)=90 By solving this equation, we can find the value of x.

2x+x-6=90

AddTerms

Add terms

3x-6=90

AddEqn

LHS+6=RHS+6

3x=96

DivEqn

.LHS /3.=.RHS /3.

x=32

Once we know the value of x, we can find the exact values of the acute angles. cc 2x& →& 2( 32)&→& 64^(∘) (x-6)&→& 32-6&→& 26^(∘)