Angles of Polygons
In these lessons, we will learn
- how to calculate the sum of interior angles of a polygon using the sum of angles in a triangle
- the formula for the sum of interior angles in a polygon
- how to solve problems using the sum of interior angles
- the formula for the sum of exterior angles in a polygon
- how to solve problems using the sum of exterior angles.
All the polygons in these lessons are assumed to be convex polygons .
Related Pages Polygons Quadrilaterals Cyclic Quadrilaterals More Geometry Lessons
The following diagrams give the formulas for the sum of the interior angles of a polygon and the sum of exterior angles of a polygon. Scroll down the page if you need more examples and explanation.
Sum Of Interior Angles Of A Polygon
We first start with a triangle (which is a polygon with the fewest number of sides). We know that
The sum of interior angles in a triangle is 180°.
This is also called the Triangle Sum Theorem. Click here if you need a proof of the Triangle Sum Theorem.
Next, we can figure out the sum of interior angles of any polygon by dividing the polygon into triangles. We can separate a polygon into triangles by drawing all the diagonals that can be drawn from one single vertex.
In the quadrilateral shown below, we can draw only one diagonal from vertex A to vertex B. So, a quadrilateral can be separated into two triangles.
The sum of angles in a triangle is 180°. Since a quadrilateral is made up of two triangles the sum of its angles would be 180° × 2 = 360°
The sum of interior angles in a quadrilateral is 360º
A pentagon (five-sided polygon) can be divided into three triangles. The sum of its angles will be 180° × 3 = 540°
The sum of interior angles in a pentagon is 540°.
A hexagon (six-sided polygon) can be divided into four triangles. The sum of its angles will be 180° × 4 = 720°
The sum of interior angles in a hexagon is 720°.
Formula For The Sum Of Interior Angles
We can see from the above examples that the number of triangles in a polygon is always two less than the number of sides of the polygon. We can then generalize the results for a n-sided polygon to get a formula to find the sum of the interior angles of any polygon.
The following diagram shows the formula for the sum of interior angles of an n-sided polygon and the size of an interior angle of a n-sided regular polygon. Scroll down the page for more examples and solutions on the interior angles of a polygon.
Example: Find the sum of the interior angles of a heptagon (7-sided)
Solution: Step 1: Write down the formula (n - 2) × 180°
Step 2: Plug in the values to get (7 - 2) × 180° = 5 × 180° = 900°
Answer: The sum of the interior angles of a heptagon (7-sided) is 900°.
Example: Find the interior angle of a regular octagon.
Answer: Each interior angle of an octagon (8-sided) is 135°.
Worksheet using the Formula for the Sum of Interior Angles
How to find the sum of the interior angles of any polygon using triangles and then derive the generalized formula?
Problems Using The Sum Of Interior Angles
How to find a missing angle using the sum of interior angles of a polygon?
How to use the sum of interior angles to write an equation and solve for the unknown? Write an equation and solve for the unknown. Substitute your answer into each expression to determine the measure of the angle. Give reasons for your answers.
Formula For The Sum Of Exterior Angles
The sum of exterior angles of any polygon is 360°.
The exterior angle of a regular n-sided polygon is 360°/n
Worksheet using the formula for the sum of exterior angles
Worksheet using the formula for the sum of interior and exterior angles
How to find the sum of the exterior angles and interior angles of a polygon? Every convex polygon has interior and exterior angles. The interior angles are inside the polygon formed by the sides. The exterior angles form a linear pair with the interior angles.
Example: Determine the measure of each exterior and interior angle of a regular polygon.
Problems using the sum of exterior angles
The following video shows a problem involving the sum of exterior angles of a polygon.
Example: A regular polygon has an exterior angle that measures 40°. How many sides does the polygon have?
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Polygon Worksheets
These worksheets focus on the topics typically covered in Geometry (no variables).
- Interior Angles of Polygons
- Exterior Angles of Polygons
- Similar Polygons
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Homework 1: Angles of Polygons ... angles of a polygon is 5400', how many sides does it have? = 11. The measure of the seven angles in a nonagon measure 1380 1540 1450, 1320 1280 1470, and 1300. If the two remaining angles are equal in measure, what is the measure of each angle?
Created Date: 12/5/2016 11:29:57 AM
Question: Name: Unit 7: Polygons & Quadrilaterals Date: Per: Homework 1: Angles of Polygons ** This is a 2-page document! ** 1. What is the sum of the measures of the interior angles of an octagon? 2. What is the sum of the measures of the interior angles of a 25-gon? 3. What is the measure of each interior angle of a regular hexagon? 4.
Unit 7 HW #1-Angles of Polygons quiz for 10th grade students. Find other quizzes for Mathematics and more on Quizizz for free! ... Show Answers. See Preview. 1. Multiple Choice. Edit. 15 minutes. 1 pt. What is the formula for the sum of interior angles in a polygon? (n−2)180 (n−2)180÷n. 360. 360/n. 2. Multiple Choice
Find solutions and answers for geometry homework problems from the textbook by McGraw-Hill Education. Browse by chapter and section to find exercises on angles of polygons and other topics.
Classify the polygon. 6840°. Find the sum of the interior angles of a convex 40-gon. 24-gon. The sum of the measures of the interior angles of a convex polygon is 3960. Classify the polygon. 121°. A convex hexagon has interior angle measures of 105°, 142°, 140°, 124°, 88° and x°. Find the value of x.
Terms in this set (17) 3 sides, 1 triangle, and 180 degrees. 4 sides, 2 triangles, 360 degrees. 5 sides, 3 triangles, 540 degrees. 6 sides, 4 triangles, and 720 degrees. 8 sides, 6 triangles, and 1080 degrees. A closed figure formed by 3 or more line segments called sides. The sum of the measures of the inferior angles in any polygon can be ...
WORKSHEET 7.1 - Angles of Polygons Name: _____ Hour: _____ Date: _____ SECTION 1: Determine if each polygon is ... SECTION 2: Calculate the sum of the interior angle measures of each polygon. 4) 5) 6) SECTION 3: Determine how many sides each polygon would have based on sum of its interior angle measures. 7) 1620° 8) 2160° 9) 9360° ...
5 S 1 §'4 =1108 =10 Sy of The EXTERIOR ANGLE Mgy Exterior angles are supplementary to their adjacent interior bngle. Find the measure of each exterior angle on the polygons below, then give the sum of all exterior angle measures. Triangle: Quadrilateral: Sum of Exterior Sum of Exterior Angles Measures: Angles Measures: 'o'o M. & 0 .
Question: Quiz 7-1: Angles of Polygons & Parallelograms Part I: Angles of Polygons 1. What is the sum of the degrees of the interior angles of a 19-gon? 2. If the sum of the interior angles of a polygon is 1800° how many sides does it have? 3. What is the measure of an interior angle of a regularnonagone 1. type 2. type 3. type 4. type 5. type 4.
Scroll down the page for more examples and solutions on the interior angles of a polygon. Example: Find the sum of the interior angles of a heptagon (7-sided) Solution: Step 1: Write down the formula (n - 2) × 180°. Step 2: Plug in the values to get (7 - 2) × 180° = 5 × 180° = 900°. Answer: The sum of the interior angles of a heptagon (7 ...
60 = 1980 180 n = 234013 = n Th. polygon has 13 sides.Example 3: How many degrees does each angle in an eq. iangular nonagon have?Solution: First we need to find the sum of the interior angles i. 2)180 = 7 180 = 1260Second, because the nonagon is equiangular.
7.1 Angles of Polygons. Term. 1 / 16. Polygon. Click the card to flip 👆. Definition. 1 / 16. a shape (closed shape w/ 3 or more sides.)
TOS. Chart Maker. Geometry Calculator. Algebra Solver. Math Games. Calculator. Free printable worksheets with answer keys on Polygons (interior angles, exterior angles etc..) Each sheet includes visual aides, model problems and many practice problems.
Use the function in part (a) to find the measure of one interior angle of a regular pentagon. Use dynamic geometry software to check your result by constructing a regular pentagon and finding the measure of one of its interior angles. Copy your table from Exploration 1 and add a row for the measure of one interior angle in a regular polygon ...
Hotmath Homework Help Math Review Math Tools Multilingual eGlossary Online Calculators Study to Go. Mathematics. Home > Chapter 6 > Lesson 1. New York Geometry. Chapter 6, Lesson 1: Angles of Polygons. Extra Examples; Personal Tutor; Self-Check Quizzes; Log In.
Example 4: The measure of each interior angle of a polygon is 150. Find the number of sides in the polygon. Let be the number of sides. Since all angles of a regular polygon are congruent, the sum of the interior angles can be expressed as 150 150 =. − 2 ∙ 180 150 = 180 − 360 −30 = −360 = 12. There are 12 sides.
The sum of the interior angles of a polygon can be calculated using the formula: (n - 2) * 180 degrees, where "n" represents the number of sides (or vertices) of the polygon. Exterior angles: An exterior angle of a polygon is an angle formed by one side of the polygon and the extension of its adjacent side. The sum of the exterior angles of any ...
For polygons that are regular we must use the following formula: x = sum of interior angles ÷ number of sides. According to the above, if we have an irregular pentagon we could calculate the sum of its internal angles as follows: x = (5 - 2) × 180°. x = 3 × 180°. x = 540°.
8 of 12. Term. To classify a quadrilateral as a parallelogram, rectangle, rhombus, or square: -All 4 angles are right angles. -Diagonals are congruent. (Prove one pair of opposite sides are congruent and parallel) Step 1: Distance formula on sides. Step 2: Distance formula on diagonals. -All 4 sides are congruent.
Expected Learning Outcomes. The students will be able to: 1) Use the interior angle measures of polygons. 2) Use the exterior angle measures of polygons. LESSON 7.1 NOTES. LESSON 7.1 RESOURCES. Download a printable version of the notes here. Download the homework worksheet here. Download the homework worksheet answers here.
1) Exactly two pairs of consecutive congruent sides. 2) One pair of opposite angles are congruent. 3) Diagonals are perpendicular. Study with Quizlet and memorize flashcards containing terms like How do you determine the Interior Angles Sum?, Polygon, Sum of Interior Angles of a Polygon Formula and more.
To find the sum of the interior angles of a polygon, you can use the formula (n-2) x 180, where n is the number of sides. For example, a quadrilateral has four sides, so the sum of its interior angles would be (4-2) x 180 = 360 degrees. Each individual angle of a quadrilateral can be found by dividing the sum of the interior angles by the ...