1. Lesson 14 Measure of the Angles of Polygons

2. Get the idea The sum of the measure of interior angles of any triangle is 180°. We can use this fact to help us figure out how many degrees are inside polygons.

3. Example 1 In Triangle ABC, angles A and C are congruent. What is the measure of <A. Use what you know about the sum of the measures of the angles in a triangle. x+90+x=180. So what does angle A equal? A B C

4. Dividing up polygons Any polygon can be divided into triangles by drawing diagonals from the same vertex. For example, a pentagon can be divided into 3 triangles. We know that the sum of the measures of the angles in each triangle in 180°. So, the sum of the measures of the angles in a pentagon is: 180x3=540°.

5. Measure of Interior Angles You can also use the following formula to find the total number of degrees in any polygon: 180(n-2) where n represents the number of sides.

6. Example 2 What is the measure of each interior angle in a regular hexagon? There are 4 triangles. Multiply 180° by the number of triangles. 180°x4= 720° There are 6 angles in a hexagon. So, 720°/6= 120°. The measure of each interior angle of a regular hexagon is 120°.

7. How do I find each angle? Another way to find the measure of each interior angle of a regular polygon is to use a formula… 180(n-2), where n represent number of sides. n

8. Tessellations A tessellation is a pattern of repeating figures in which there are no gaps between the figures. A regular polygon can be used to create a tessellation IF the measure of each interior angle evenly divides 360°. If the measure of the angle does not divide into 360°, there will be gaps in the shapes when you put them together. What is an example of a tessellation in everyday life?

9. An example What shape is tessellating? 360°

10. Example Randy wants to create a tessellation using only regular octagons. Is that possible? – Use the formula 180(n-2). n – Find the measure of each angle. – Does it divide into 360°? – Does it tessellate?

11. Practice time Complete pg 92 and 93 in the Coach book in groups. We will complete the open-ended together.