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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 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. .
Got questions? Get instant answers now!
Got questions? Get instant answers now!

An angle measures 25° . Find its: supplement complement.

  1. 155°
  2. 65°

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An angle measures 77° . Find its: supplement complement.

  1. 103°
  2. 13°

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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 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. .
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Two angles are supplementary. The larger angle is 100° more than the smaller angle. Find the measures of both angles.

40°, 140°

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Two angles are complementary. The larger angle is 40° more than the smaller angle. Find the measures of both angles.

25°, 65°

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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 Δ A B C , read ‘triangle ABC ’. We label each side with a lower case letter to match the upper case letter of the opposite vertex.

The vertices of the triangle on the left are labeled A, B, and C. The sides are labeled a, b, and c.
Δ A B C has vertices A , B , and C and sides a , b , and c .

The three angles of a triangle are related in a special way. The sum of their measures is 180° .

m A + m B + m C = 180°

Sum of the measures of the angles of a triangle

For any Δ A B C , the sum of the measures of the angles is 180° .

m A + m B + m C = 180°

The measures of two angles of a triangle are 55° and 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. .
Got questions? Get instant answers now!
Got questions? Get instant answers now!

The measures of two angles of a triangle are 31° and 128° . Find the measure of the third angle.

21°

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A triangle has angles of 49° and 75° . Find the measure of the third angle.

56°

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Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
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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.
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this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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Practice Key Terms 9

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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