the measure of angle 1 is twice the measure of angle 2. the measure of angle 3 is 40 degrees less than the measure of angle 2. which of the following tools would you use to determine the measures of the three angles? justify your selection(s). then use the tool(s) to solve the problem.
draw a model
paper/pencil
calculator
To determine the measures of the three angles, you can use a combination of drawing a model and paper/pencil.
1. Draw a Model:
Drawing a model is an effective way to visualize the problem. You can draw three angles with their corresponding measurements, as described in the problem statement. This will help you analyze the relationships and solve for the unknowns.
2. Paper/Pencil:
Using a pencil and paper allows you to perform mathematical calculations and record your work neatly. You will need to set up and solve equations based on the given information about the angles.
Calculators are not necessary for this problem since it involves basic arithmetic and algebraic manipulation, which can be easily done by hand.
Now, let's solve the problem using the selected tools:
Let the measure of angle 2 be x degrees.
According to the problem statement:
- Angle 1 is twice the measure of angle 2, so angle 1 = 2x degrees.
- Angle 3 is 40 degrees less than the measure of angle 2, so angle 3 = x - 40 degrees.
Since the sum of angles in a triangle is 180 degrees, we can write the equation:
angle 1 + angle 2 + angle 3 = 180
2x + x + (x - 40) = 180
Combining like terms, we have:
4x - 40 = 180
Solving for x, we get:
4x = 180 + 40
4x = 220
x = 55
Now, substituting the value of x back into the expressions for the angles:
angle 1 = 2x = 2 * 55 = 110 degrees
angle 2 = x = 55 degrees
angle 3 = x - 40 = 55 - 40 = 15 degrees
So, the measures of the three angles are:
angle 1 = 110 degrees
angle 2 = 55 degrees
angle 3 = 15 degrees
I would use algebra
the actual calculations can then be done mentally.
let angle 2 = x
let angle 1 = 2x
let angle 3 = 2x-40
2x-40 + 2x + x = 180
etc.