8 4 Angles in Polygons Warm Up Problem

8 -4 Angles in Polygons Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

8 -4 Angles in Polygons Math Journal (5 Min) • K-W-L - Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write the “K” what they know and “W” what they want to know about the lesson before they have been taught the lesson, and at the end of class, write the “L” what they now know (Learned) about the lesson after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that they learned that pertained to the lesson.

8 -4 Angles in Polygons Homework Review (5 Min)

8 -4 Angles in Polygons Warm Up Solve. 1. 72 + 18 + x = 180 2. 80 + 70 + x = 180 x = 90 x = 30 3. x + 42 + 90 = 180 x = 48 4. 120 + x + 32 = 180 x = 28

8 -4 Angles in Polygons Problem of the Day How many different rectangles are in the figure shown? 100

8 -4 Angles in Polygons Textbook Examples (I Do) (5 Min)

8 -4 Angles in Polygons Learn to find the measures of angles in polygons.

8 -4 Angles in Polygons Vocabulary diagonal

8 -4 Angles in Polygons If you tear off the corners of a triangle and put them together, you will find that they form a straight angle. This suggests that the sum of the measures of the angles in a triangle is 180°.

8 -4 Angles in Polygons

8 -4 Angles in Polygons Additional Example 1: Finding an Angle Measure of in a Triangle Find the measure of the unknown angle. 55° 80° x 80° + 55° + x = 180° The sum of the measures of the angles is 180°. 135° + x = 180° Combine like terms. – 135° Subtract 135° from both sides. x = 45° The measure of the unknown angle is 45°.

8 -4 Angles in Polygons Check It Out: Example 1 Find the measure of the unknown angle. 30° 90° x 90° + 30° + x = 180° The sum of the measures of the angles is 180°. 120° + x = 180° Combine like terms. – 120° Subtract 120° from both sides. x = 60° The measure of the unknown angle is 60°.

8 -4 Angles in Polygons A diagonal is a line segment that connects two non-adjacent vertices of a polygon. Since the sum of the angle measures in each triangle is 180°, the sum of the angle measures in a foursided figure is 2 · 180°, or 360°. Diagonal

8 -4 Angles in Polygons

8 -4 Angles in Polygons Additional Example 2: Finding an Angle Measure of in a Quadrilateral 89° Find the unknown angle measure in the quadrilateral. 82° 65° + 89° + 82° + x = 360° 236° + x = 360° – 236° x = 124° x The sum of the measures of the angles is 360°. Combine like terms. Subtract 236° from both sides. The measure of the unknown angle is 124°.

8 -4 Angles in Polygons Check It Out: Example 2 92° Find the unknown angle measure in the quadrilateral. 67° + 92° + 89° + x = 360° 248° + x = 360° – 248° x = 112° 89° 67° x The sum of the measures of the angles is 360°. Combine like terms. Subtract 248° from both sides. The measure of the unknown angle is 112°.

8 -4 Angles in Polygons In a convex polygon, all diagonals can be drawn within the interior of the figure. By dividing any convex polygon into triangles, you can find the sum of its interior angle measures.

8 -4 Angles in Polygons Additional Example 3: Drawing Triangles to Find the Sum of Interior Angles Divide each polygon into triangles to find the sum of its angle measures. 6 · 180° = 1080° There are 6 triangles. The sum of the angle measures of an octagon is 1, 080°.

8 -4 Angles in Polygons Check It Out: Example 3 Divide each polygon into triangles to find the sum of its angle measures. 4 · 180° = 720° There are 4 triangles. The sum of the angle measures of a hexagon is 720°.

8 -4 Angles in Polygons Class work Problems (We Do) (10 Min) • Pg. 332 -333 (1 -9)

8 -4 Angles in Polygons

8 -4 Angles in Polygons Small Group CW(Yall Do) (10 Min) • Pg. 332 -333 (10 -28 EOE)

8 -4 Angles in Polygons

8 -4 Angles in Polygons Homework (You Do) (10 Min) • Pg. 332 -333 (11, 13, 17, 19, 21 odd)

8 -4 Angles in Polygons Math Journal (5 Min) • K-W-L - Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write the “K” what they know and “W” what they want to know about the lesson before they have been taught the lesson, and at the end of class, write the “L” what they now know (Learned) about the lesson after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that they learned that pertained to the lesson.

8 -4 Angles in Polygons Lesson Quizzes Standard Lesson Quiz for Student Response Systems

8 -4 Angles in Polygons Lesson Quiz Find the measure of the unknown angle for each of the following. 1. a triangle with angle measures of 66° and 77° 37° 2. a right triangle with one angle measure of 36° 54° 3. an quadrilateral with angle measures of 144°, 84°, and 48°. 84° 4. Divide a six-sided polygon into triangles to find the sum of its interior angles 720°

8 -4 Angles in Polygons Lesson Quiz for Student Response Systems 1. Identify the measure of the unknown angle for a triangle with angle measures of 35° and 53°. A. 55° B. 92° C. 268° D. 272°

8 -4 Angles in Polygons Lesson Quiz for Student Response Systems 2. Identify the measure of the unknown angle for a right triangle with one angle measure of 62°. A. 242° B. 118° C. 28° D. 18°

8 -4 Angles in Polygons Lesson Quiz for Student Response Systems 3. Divide a nine-sided polygon into triangles to identify the sum of its interior angles. A. 1080° B. 1260° C. 1440° D. 1620°