# 9.3 Use properties of angles, triangles, and the pythagorean theorem  (Page 2/15)

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The next example will show how you can use the Problem Solving Strategy for Geometry Applications to answer questions about supplementary and complementary angles.

An angle measures $\text{40°}.$ Find its supplement, and its complement.

## Solution

 ⓐ Step 1. Read the problem. Draw the figure and label it with the given information. Step 2. Identify what you are looking for. Step 3. Name. Choose a variable to represent it. Step 4. Translate. Write the appropriate formula for the situation and substitute in the given information. Step 5. Solve the equation. Step 6. Check: Step 7. Answer the question.
 ⓑ Step 1. Read the problem. Draw the figure and label it with the given information. Step 2. Identify what you are looking for. Step 3. Name. Choose a variable to represent it. Step 4. Translate. Write the appropriate formula for the situation and substitute in the given information. Step 5. Solve the equation. Step 6. Check: Step 7. Answer the question.

An angle measures $\text{25°}.$ Find its: supplement complement.

1. 155°
2. 65°

An angle measures $\text{77°}.$ Find its: supplement complement.

1. 103°
2. 13°

Did you notice that the words complementary and supplementary are in alphabetical order just like $90$ and $180$ are in numerical order?

Two angles are supplementary. The larger angle is $\text{30°}$ more than the smaller angle. Find the measure of both angles.

## Solution

 Step 1. Read the problem. Draw the figure and label it with the given information. Step 2. Identify what you are looking for. Step 3. Name. Choose a variable to represent it. The larger angle is 30° more than the smaller angle. Step 4. Translate. Write the appropriate formula and substitute. Step 5. Solve the equation. Step 6. Check: Step 7. Answer the question.

Two angles are supplementary. The larger angle is $\text{100°}$ more than the smaller angle. Find the measures of both angles.

40°, 140°

Two angles are complementary. The larger angle is $\text{40°}$ more than the smaller angle. Find the measures of both angles.

25°, 65°

## Use the properties of triangles

What do you already know about triangles? Triangle have three sides and three angles. Triangles are named by their vertices. The triangle    in [link] is called $\text{Δ}ABC,$ read ‘triangle $\text{ABC}$ ’. We label each side with a lower case letter to match the upper case letter of the opposite vertex.

The three angles of a triangle are related in a special way. The sum of their measures is $\text{180°}.$

$m\text{∠}A+m\text{∠}B+m\text{∠}C=\text{180°}$

## Sum of the measures of the angles of a triangle

For any $\text{Δ}ABC,$ the sum of the measures of the angles is $\text{180°}.$

$m\text{∠}A+m\text{∠}B+m\text{∠}C=\text{180°}$

The measures of two angles of a triangle are $\text{55°}$ and $\text{82°}.$ Find the measure of the third angle.

## Solution

 Step 1. Read the problem. Draw the figure and label it with the given information. Step 2. Identify what you are looking for. Step 3. Name. Choose a variable to represent it. Step 4. Translate. Write the appropriate formula and substitute. Step 5. Solve the equation. Step 6. Check: Step 7. Answer the question.

The measures of two angles of a triangle are $\text{31°}$ and $\text{128°}.$ Find the measure of the third angle.

21°

A triangle has angles of $\text{49°}$ and $\text{75°}.$ Find the measure of the third angle.

56°

#### Questions & Answers

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Maciej
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s.
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
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Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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Cied
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Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
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Yasmin
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Prasenjit
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Uday
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