What are the major theorems that allow you to determine the relationships between angles formed by

lines that intersect a circle?

You can determine the measure of an inscribed angle by multiplying the measure of its intercepted arc

. You can use the (select)

Theorem to find missing angle measures.

A)

Valerie measured 4 walls at 2 1/2 feet. In decimal form, each wall is 2.5 feet long. So, the total length of the 4 walls is (2.5 × 4) feet.

Valerie measured 3 walls at 21 1/4 feet. In decimal form, each wall is 21.25 feet long. So, the total length of the 3 walls is (21.25 × 3) feet.

Valerie measured 1 wall at 32 feet.

The expression that gives the total length of the walls that Valerie measured is (2.5 × 4) + (21.25 × 3) + 32.

B)

Seth measured 1 wall at 3.5 feet.

Seth measured 2 walls at 22.75 feet. So, the total length of the 2 walls is (22.75 × 2) feet.

Seth measured 1 wall at 58 feet.

The expression that gives the total length of the walls that Seth measured is 3.5 + (22.75 × 2) + 58.

C)

The total length of Valerie’s walls is (2.5 × 4) + (21.25 × 3) + 32.

The total length of Seth’s walls is 3.5 + (22.75 × 2) + 58.

To find the expression for the perimeter of the house, add Valerie’s expression to Seth’s:

(2.5 × 4) + (21.25 × 3) + 32 + 3.5 + (22.75 × 2) + 58.

D)

(2.5 × 4) + (21.25 × 3) + 32 + 3.5 + (22.75 × 2) + 58

= 10 + 63.75 + 32 + 3.5 + 45.5 + 58

= 212.75

The perimeter of the house is 212.75 feet.

E)

The total length of Valerie’s walls is 105.75 feet:

(2.5 × 4) + (21.25 × 3) + 32 = 10 + 63.75 + 32 = 105.75 feet.

The total length of Seth’s walls is 107 feet:

3.5 + (22.75 × 2) + 58 = 3.5 + 45.5 + 58 = 107 feet.

The sum of 105.75 feet and 107 feet is 212.75 feet. The Commutative Property allows me to add numbers in any order. This is why the answers in parts D and E match.

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