Measurement of Angles Level 6 In this video we will go over more examples
involving parts of a degree and congruent angles.
Let’s jump straight into the first example.
Find the measure of the angle formed by the hands of a clock at each time.
3:00 In this problem we are asked to determine
the measurement of an angle formed between the hour and minute hand at particular times.
Let’s first draw a clock and determine the degree measurement between each hour.
A typical clock can be modeled by using a circle and dividing it into 12 equal slices
each slice corresponds to a single hour.
Since a revolution around a circle corresponds to a degree measurement of 360 degrees, each
slice will be equal to 30 degrees.
The number 12 is usually assigned to the top position on the circle and the numbers 1 through
11 are assigned to each subsequent boundary of each slice as we move clockwise around
the circle.
The minute hand starts at the border where the number 12 is assigned and this position
represents 0 minutes, this hand will move clockwise and will cover 5 minutes as it moves
border to border.
Another thing to keep in mind is that the hour hand will be located at the border of
each slice only when the minute hand is on the border where the number 12 is assigned.
As the minute hand moves clockwise, the hour hand will slowly start moving towards the
border of the next slice so we have to take this into account as we measure the angles
between the hands.
At 3:00 o’clock the minute hand is located at the border where the number 12 is assigned.
The hour hand is located at the border where hour 3 is assigned.
Since there are 3 slices between the hands, the angle measure would be 30 degrees times
3 or in this case 90 degrees.
Let’s try the next example.
4:30 At 4:30 the minute hand is located at the
border where the number 6 is assigned.
Now, the hour hand will not be located at the border where the number 4 is assigned
since the minute hand is no longer located at the border where the number 12 is assigned.
When the minute hand is at 6, the hour hand is one half of the way from 4 to 5.
So taking this into consideration we see that there are 1 and a half slices between the hands,
so the angle formed is 30 plus 15 degrees, which simplifies to 45 degrees.
Alright let’s try the next problem.
7:20 At 7:20 the minute hand is located at the
border where the number 4 is assigned.
The hour hand is going to be between 7 and 8.
Since the minute hand is one third of the way around the circle, the hour hand will
also be one third of the way between 7 and 8.
So there are 3 and a third slices between the hands, the angle formed will be 90 degrees
plus 10 degrees, which simplifies to 100 degrees.
Let’s move along to the next example.
1:45 At 1:45 the minute hand is located at the
border where the number 9 is assigned and the hour hand is going to be located somewhere
between 1 and 2.
In this case the hour hand will be three quarters of the way between 1 and 2.
We will use the smallest angle between the hands.
So there are 4 and three quarter slices between the hands, the angle formed will be 120 degrees
plus 22.5 degrees, which simplifies to 142.5 degrees or 142 degrees 30 minutes.
Alright, let’s end the video by going over a different type of problem.
In the diagram below, the measurement of angle DEG is 80 degrees, the measurement of angle
DEF is 50 degrees, the measurement of angle HJM is 120 degrees, and the measurement of
angle HJK is 90 degrees.
Draw a conclusion about angle FEG and angle KJM.
In this problem we are provided with two diagrams and are given the measurement of various angles,
we are asked to draw a conclusion about the relationship between 2 particular angles.
Let’s start the problem by labeling all the given angles in the diagram this way we
can visually see the location and value of all the angles.
Angle DEG measures 80 degrees, and angle DEF measures 50 degrees,
angle HJM measures 120 degrees
and angle HJK measures 90 degrees, we can draw a small corner for this angle instead
of writing 90 degrees since it is a right angle.
Now we need to draw a conclusion between angle FEG and angle KJM.
Before we can do this, we need to know the measurement of both of these angles.
To determine the measurement of angle FEG we can take the measurement of angle DEG and
subtract the measurement of angle DEF doing that we obtain 30 degrees.
Similarly to determine the measurement of angle KJM we can take the measurement of angle
HJM and subtract the measurement of angle HJK doing that we also obtain 30 degrees.
Since both of these angles have the same measurement we can conclude that angle FEG is congruent
to angle KJM and this is our final answer.
Alright, in our next video we will go over more challenging examples
involving congruent angles with algebraic expressions.