Exercise 55 Page 594

From the two figures, we see that ∠ ABC ≅ ∠ KHG. This means we can equate the expressions of these angles. ∠ ABC ≅ ∠ KHG: 6x^(∘)+2^(∘)=(5x^(∘)-27^(∘))+(3x^(∘)+1^(∘))Since the equation only contains x as a variable, it can be solved.

6x^(∘)+2^(∘)=(5x^(∘)-27^(∘))+(3x^(∘)+1^(∘))

▼

Solve for x

RemovePar

Remove parentheses

6x^(∘)+2^(∘)=5x^(∘)-27^(∘)+3x^(∘)+1^(∘)

SimpTerms

Simplify terms

6x^(∘)+2^(∘)=8x^(∘)-26^(∘)

AddEqn

LHS+26^(∘)=RHS+26^(∘)

6x^(∘)+28^(∘)=8x^(∘)

SubEqn

LHS-6x^(∘)=RHS-6x^(∘)

28^(∘)=2x^(∘)

DivEqn

.LHS /2.=.RHS /2.

14^(∘)=x^(∘)

RearrangeEqn

Rearrange equation

x^(∘)=14^(∘)

When we know that x^(∘)= 14^(∘) we can substitute this into the expression for ∠ ABC. ∠ ABC: 6( 14^(∘))+2^(∘)=86^(∘)