Exercise 13 Page 737

By Congruent Corresponding Chords Theorem in the same circle two minor arcs are congruent if and only if their corresponding chords are congruent.

Practice makes perfect

We will find the value of x. Notice that the two circles are congruent according to the exercise.

Let's recall the Congruent Corresponding Chords Theorem.

Congruent Corresponding Chords Theorem
In congruent circles two minor arcs are congruent if and only if their corresponding chords are congruent.

We know that chords KL and AJ are congruent. By the theorem the corresponding minor arcs are also congruent. 5x^(∘)=(3x+54)^(∘) Let's solve this equation for x.

5x^(∘)=(3x+54)^(∘)

RemovePar

Remove parentheses

5x^(∘)=3x^(∘)+54^(∘)

SubEqn

LHS-3x^(∘)=RHS-3x^(∘)

2x^(∘)=54^(∘)

DivEqn

.LHS /2.=.RHS /2.

x^(∘)=27^(∘)

Subchapter links

Exercises p.736-740

Exercise 13 Page 737

Hints

Check the answer

Practice exercises

Assess your skill