Exercise 22 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 Triangle Angle-Sum Theorem, which states that acute angles of a right triangle are complementary. In this case, it means that 11x-2 and 6x+7 add up to 90. (19x-1)+(13x-5)=90 By solving this equation, we can find the value of x.

19x-1+13x-5=90

AddSubTerms

Add and subtract terms

32x-6=90

AddEqn

LHS+6=RHS+6

32x=96

DivEqn

.LHS /32.=.RHS /32.

x=3

Once we know the value of x, we can find the exact values of the acute angles. cc 19x-1& →& 19( 3)-1&→& 56^(∘) 13x-5&→&13( 3)-5&→& 34^(∘)