Measurement of Angles Level 9 In this final video on measurement of angles
we will go over 2 final examples that require the use of algebra to solve.
Let's take a look at the first example.
If angle POA is a right angle and if the measurement of angle POC is three times as large as the
measurement of angle COA.
Find the measure of angle POC.
In this problem we are provided with a figure along with geometric and algebraic relations
of two angles.
We are asked to find the measure of a particular angle.
We know from the problem that the measurement of angle POC is three times as large as the
measurement of angle COA.
So if we use the variable x to represent the measure of angle COA then the measure of angle
POC can be expressed as 3x.
From the diagram we know that the measure of angle POC plus the measure of angle COA
is equal to the measure of angle POA.
Using this geometric relation we can go ahead and substitute the algebraic and numeric expression
for the measurement of the angles.
We also know that angle POA is a right angle so we can replace the measure of this angle
with 90 degrees.
Now it is just a matter of solving for x, doing that we obtain x equals 22.5.
We can now use this value to determine the measurement of angle POC, substituting this
value into the algebraic expression and simplifying we obtain 67.5 degrees for the measurement
of angle POC and this is our final answer.
All right let's move along to the next example.
Given that angle TRS is a straight angle, angle TRX is a right angle, the measure of
angle TRS is 2x plus 5y, and the measure of angle XRS is 3x plus 3y solve for x and y.
In this problem we are provided with a figure along with 2 algebraic expressions one for
each angle.
We are asked to determine the values of x and y.
Notice that in this problem we actually want to solve for x and y just like we did in our
introductory algebra class.
The only difference is that we need to use the geometric relations to set up an equation
and solve for the variables.
Let's first label the diagram with the given information, we know that angle TRS is a straight
angle and measures 2x plus 5y.
We also know that angle TRX is a right angle.
So we go ahead and draw a square corner for this angle.
Since angle TRS is a straight angle the sum of the measure of angle TRX and XRS must equal
180 degrees.
Since the measure of angle TRX is 90 degrees we can conclude that the measure of angle
XRS is also 90 degrees.
Hence both angles are congruent meaning that both have the same measurement so the measurement
of angle XRS is 90 degrees.
Now we can equate the algebraic expression for the measurement of angle XRS with 90 degrees.
Notice that we now have 2 equations and 2 unknowns, at this point the problem becomes
a system of equations problem similar to the once covered in a typical beginning algebra
course.
Again if you are bit rusty on this topic I recommend you go back and review this topic.
We are going to use the elimination method to solve this system.
In this case we will eliminate the variable x.
So we need to multiply the first equation by 3 and multiply the second equation by negative
2, doing that we obtain the following.
Next we go ahead and add the equations.
Now that we have an equation with a single variable we go ahead and solve for y, simplifying
the expression we obtain 40.
The last step is to substitute this value into one of the original equations and solve
for the variable x.
Let's substitute this value into the second equation, solving for x and simplifying we
obtain negative 10 for the value of x.
So x equals negative 10 and y equals 40 so this is our final answer.
All right and we are now officially done with the measurement of angles video series.
In our next series of videos we will go over the concept of collinearity.
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