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Transcript
Lesson 14 Measure of the Angles of Polygons 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. Example 1 • In Triangle ABC, angles A and C are congruent. What is the measure of <A. A B C • 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? 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°. 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. 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°. 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 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? An example • What shape is tessellating? 360° 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? Practice time • Complete pg 92 and 93 in the Coach book in groups. • We will complete the open-ended together.