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McGraw Hill Integrated II, 2012 View details

3. Arcs and Chords

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Exercise 10 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.

Let's recall the Congruent Corresponding Chords Theorem.

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

We know that chords WY and YZ are congruent. By the theorem the corresponding minor arcs are also congruent. 143^(∘)=(2x-1)^(∘) Let's solve the equation to obtain the value of x.

143^(∘)=(2x-1)^(∘)

▼

Solve for x^(∘)

RemovePar

Remove parentheses

143^(∘)=2x^(∘)-1^(∘)

AddEqn

LHS+1^(∘)=RHS+1^(∘)

144^(∘)=2x^(∘)

DivEqn

.LHS /2.=.RHS /2.

72^(∘)=x^(∘)