Answer:
43 DEGREES
Step-by-step explanation:
In this section we will use some common geometry formulas. We will adapt our problem-solving strategy so that we can solve geometry applications. The geometry formula will name the variables and give us the equation to solve. In addition, since these applications will all involve shapes of some sort, most people find it helpful to draw a figure and label it with the given information. We will include this in the first step of the problem solving strategy for geometry applications.
Solve Geometry Applications.
Read the problem and make sure all the words and ideas are understood. Draw the figure and label it with the given information.
Identify what we are looking for.
Label what we are looking for by choosing a variable to represent it.
Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
Solve the equation using good algebra techniques.
Check the answer by substituting it back into the equation solved in step 5 and by making sure it makes sense in the context of the problem.
Answer the question with a complete sentence.
We will start geometry applications by looking at the properties of triangles. Let’s review some basic facts about triangles. Triangles have three sides and three interior angles. Usually each side is labeled with a lowercase letter to match the uppercase letter of the opposite vertex.
The plural of the word vertex is vertices. All triangles have three vertices. Triangles are named by their vertices: The triangle in (Figure) is called
Triangle ABC has vertices A, B, and C. The lengths of the sides are a, b, and c.
The three angles of a triangle are related in a special way. The sum of their measures is Note that we read as “the measure of angle A.” So in in (Figure),
Because the perimeter of a figure is the length of its boundary, the perimeter of is the sum of the lengths of its three sides.
To find the area of a triangle, we need to know its base and height. The height is a line that connects the base to the opposite vertex and makes a angle with the base. We will draw again, and now show the height, h. See (Figure).
The formula for the area of is where b is the base and h is the height.
Triangle Properties
For
Angle measures:
The sum of the measures of the angles of a triangle is
Perimeter:
The perimeter is the sum of the lengths of the sides of the triangle.
Area:
The area of a triangle is one-half the base times the height.
The measures of two angles of a triangle are 55 and 82 degrees. 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. the measure of the third angle in a triangle
Step 3. Name. Choose a variable to represent it. Let the measure of the angle.
Step 4. Translate.
Write the appropriate formula and substitute.
Step 5. Solve the equation.
Step 6. Check.
Step 7. Answer the question. The measure of the third angle is 43 degrees.
