2 Missing Angles in a Polygon
Summary
TLDRIn this video, the presenter demonstrates how to calculate a missing angle in a polygon. Using the formula (n-2) * 180, they determine the total degrees in a five-sided pentagon to be 540°. By subtracting the known angles (112°, 130°, 96°, and 105°) from the total, the missing angle is calculated to be 97°. The video emphasizes checking the work by adding all angles to ensure they sum to 540°.
Takeaways
- 📝 The video demonstrates how to find a missing angle in a polygon.
- 📏 It begins by recalling the formula (n - 2) * 180 to determine the total degrees in a polygon.
- 🔺 For this example, a pentagon (5-sided shape) is used.
- 🔢 The calculation starts with n = 5, leading to (5 - 2) * 180 = 540°.
- 📐 This means the total internal angles of the pentagon add up to 540°.
- ➖ To find the missing angle, subtract the known angles from 540°.
- ✏️ The known angles are: 112°, 130°, 96°, and 105°.
- 🔍 Subtracting these from 540° leaves the missing angle, y, which is calculated to be 97°.
- ✅ The result is verified by ensuring the sum of all angles equals 540°.
- 🔚 The method is summarized: use the total degree formula, subtract known angles, and check the sum for accuracy.
Q & A
What is the formula used to find the total sum of interior angles in a polygon?
-The formula is (n - 2) * 180, where n is the number of sides in the polygon.
How many sides does the polygon in the example have?
-The polygon in the example is a pentagon, which has 5 sides.
How do you calculate the total sum of the interior angles for a pentagon?
-For a pentagon, n is 5. Using the formula (n - 2) * 180, we get (5 - 2) * 180 = 3 * 180 = 540 degrees.
What is the first step in finding the missing angle in the polygon?
-The first step is to calculate the total sum of the interior angles of the polygon using the formula.
How do you determine the missing angle once you have the total sum of the interior angles?
-Subtract the sum of the known angles from the total sum of the interior angles.
What are the known angles in the example provided?
-The known angles are 112 degrees, 130 degrees, 96 degrees, and 105 degrees.
How do you find the value of the missing angle?
-Subtract the sum of the known angles from 540 degrees: 540 - (112 + 130 + 96 + 105).
What is the value of the missing angle in the example?
-The missing angle is 97 degrees.
How can you verify the correctness of the calculated missing angle?
-Add the missing angle to the known angles and ensure the total is 540 degrees.
What should you do if the sum of the angles does not equal the total calculated sum of interior angles?
-If the sum is incorrect, recheck your calculations for any errors in the steps.
Outlines
📐 Introduction to Finding a Missing Angle in a Polygon
In this video, the instructor introduces the topic of calculating a missing angle in a polygon. The formula (n-2) * 180 is used to determine the total degrees in a polygon. The example focuses on a pentagon, a five-sided shape.
🔢 Calculating the Total Degrees in a Pentagon
The first step involves calculating the total degrees in a pentagon. Since the shape has five sides, the calculation is (5-2) * 180, resulting in 540 degrees. This means the sum of all internal angles in the pentagon is 540 degrees.
➖ Subtracting Known Angles to Find the Missing Angle
The next step is to subtract the known angles from the total degrees to find the missing angle. The instructor subtracts the angles 112, 130, 96, and 105 from 540. This process leaves the missing angle, Y, which is calculated as 97 degrees.
✅ Verifying the Calculation of the Missing Angle
To ensure the calculation is correct, the instructor suggests adding all the angles (including the missing one) to check if they total 540 degrees. If the sum is correct, it verifies that the missing angle has been accurately determined.
📊 Summary and Conclusion
The video concludes with a recap of the steps taken: using the formula to find the total degrees in a polygon, subtracting known angles, and verifying the result. The example demonstrated results in finding the missing angle in a pentagon to be 97 degrees.
Mindmap
Keywords
💡Polygon
💡Missing Angle
💡Formula
💡Pentagon
💡Total Amount of Degrees
💡Calculation
💡Known Angles
💡Subtraction
💡Degrees
💡Check
💡Example
Highlights
Explanation of finding a missing angle in a polygon.
Recap of using the formula (n-2) * 180 to find the total degrees in a polygon.
Example given using a pentagon (five-sided shape).
Initial step: Identify the number of sides (n=5).
Calculation of total degrees in the pentagon: (5-2) * 180 = 540°.
Strategy for finding the missing angle: Subtract known angles from the total.
List of known angles: 112°, 130°, 96°, 105°.
Total of known angles: 112 + 130 + 96 + 105 = 443°.
Subtracting the total of known angles from 540°.
Calculation: 540 - 443 = 97°.
Verification step: Sum of all angles including the calculated one should equal 540°.
Recap of the process with the example: Total degrees, subtract known angles, find the missing angle.
Encouragement to check calculations for accuracy.
Example verifies correct calculation: 97 + 112 + 130 + 96 + 105 = 540°.
Concluding the explanation with a thank you.
Transcripts
hello in this video I'm going to show
you how we can work out a missing angle
from a
polygon in the last video we learned how
to use the formula nus 2 * by 180 to
find out the total amount of degrees
that are going to be in a
polygon for this example that I've got
here I've got a pentagon of five-sided
shape so to begin with my very first
step is to look at how many angles
there's going to be in total in this
whole shape then I can work out what
that missing angle is going to
be so like I said I've got five-sided
shape so n is going to be five so I've
got five takeway Two Times by
180 which gives me 3 lots of
180 which is
540° so I know that the total amount of
angles in this shape is going to add up
up to
540 so I need to work out what's missing
there's a few ways you can do this but
I'm going to show you the way that I
like to do it so I'm going to start off
with the total amount of angles so I've
got
540° and then I'm going to take away all
of the angles that I know added together
so I'm going to take away
112 and I'm going to take away
130 and then 96
and then
105 and then when I work that out that's
going to tell me what my missing angle Y
is when I put that in the calculator to
work it out I get y =
97
degrees once you end up with your
answer you can always check that you are
along the right lines because if you
added 97 112 130 96 and 105 you should
end up getting to
540 if you don't then you've probably
done something wrong in this part of
your workings
here so for this example at a five-sided
shape we put n is five into this
formula multiplied by 180 to get the
total amount of degrees in this shape
then I took away all of the degrees that
I know to end up with 97 as my final
answer thank you for watching goodbye
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