2 Missing Angles in a Polygon

Summary

In 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

00:00

📐 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.

Keywords

💡Polygon

A polygon is a two-dimensional shape with a finite number of straight sides and angles. It is the basic geometric figure discussed in the video, where the focus is on finding the sum of interior angles. The video specifically mentions a pentagon, which is a polygon with five sides, as an example to demonstrate the calculation of missing angles.

💡Missing Angle

A missing angle refers to an angle in a polygon whose measure is not known and needs to be determined. In the context of the video, the presenter is teaching how to calculate the measure of a missing angle in a pentagon by using the total sum of angles in the polygon and subtracting the known angles.

💡Formula

In mathematics, a formula is a concise way of expressing information symbolically, as in a mathematical proposition or theoretical model. The video script introduces the formula '(n - 2) * 180' for calculating the total sum of interior angles of any polygon, where 'n' represents the number of sides.

💡Pentagon

A pentagon is a specific type of polygon with exactly five sides and five angles. The video uses a pentagon as an example to illustrate the process of finding a missing angle by applying the general formula for the sum of interior angles of polygons.

💡Total Amount of Degrees

This term refers to the sum of all the interior angles of a polygon. The video explains that for any polygon, this sum can be calculated using the formula mentioned, and in the case of a pentagon, it amounts to 540 degrees.

💡Calculation

Calculation is the process of computing or determining something by mathematical methods. The video demonstrates a step-by-step calculation to find the measure of a missing angle in a pentagon by subtracting the known angles from the total sum of degrees.

💡Known Angles

Known angles are the measures of angles in a polygon that have already been identified or given. In the script, the presenter lists known angles (112, 130, 96, and 105 degrees) to find the missing angle by subtraction from the total.

💡Subtraction

Subtraction is one of the basic arithmetic operations, used here to find the missing angle by taking the total sum of degrees and subtracting the sum of the known angles. The script uses this method to calculate the missing angle in the pentagon.

💡Degrees

Degrees are a unit of measurement for angles, with a full circle being 360 degrees. The video script uses degrees to express the measures of the angles in the pentagon and to calculate the total sum of interior angles.

💡Check

To check in this context means to verify or confirm the accuracy of the calculation. The video suggests adding all the angles including the found missing angle to ensure they sum up to 540 degrees, which would confirm the correctness of the calculation.

💡Example

An example in an educational context is a specific case or scenario used to illustrate a concept or principle. The video provides a practical example of a pentagon to demonstrate the process of finding a missing angle using the polygon angle sum formula.

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