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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

3. Arcs and Chords

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Exercise 46 Page 740

The sum of the measures of the central angles of a circle with no interior points in common is 360^(∘).

152^(∘)

Practice makes perfect

A central angle of a circle is an angle with the vertex in the center of the circle. Also, recall that vertical angles have the same measure.

The sum of the measures of the central angles of a circle with no interior points in common is 360^(∘). With this information, we can write an equation in terms of x^(∘). x^(∘)+28^(∘)+x^(∘)+28^(∘)=360^(∘) Finally, we can solve our equation for x^(∘).

x^(∘)+28^(∘)+x^(∘)+28^(∘)=360^(∘)

Add terms

2x^(∘)+56^(∘)=360^(∘)

LHS-56^(∘)=RHS-56^(∘)

2x^(∘)=304^(∘)

.LHS /2.=.RHS /2.

x^(∘)=152^(∘)

Subchapter links

Exercises p.736-740