Exercise 19 Page 236

Let's analyze the given triangle.

As we can see, one of its angles is a right angle. Therefore, it is a right triangle. This allows us to use the corollary to the Triangle Angle-Sum Theorem, which states that acute angles of a right triangle are complementary. In this case, it means that 3x and 2x add up to 90. 3x+2x=90 By solving this equation, we can find the value of x.

3x+2x=90

AddTerms

Add terms

5x=90

DivEqn

.LHS /5.=.RHS /5.

x=18

Once we know the value of x, we can find the exact values of the acute angles. cc 3x& →& 3( 18)&→& 54^(∘) 2x&→& 2( 18)&→& 36^(∘)