Warm-Up Exercises. 1. If the measures of two angles of a triangle are 19º and 80º, find the measure of the third angle. ANSWER 81º
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1 Warm-Up Exercises 1. If the measures of two angles of a triangle are 19º and 80º, find the measure of the third angle. 81º 2. Solve (x 2)180 =
2 Warm-Up Exercises 3. Find the value of x. 126
3 EXAMPLE Warm-Up 1Exercises Find the sum of angle measures in a polygon Find the sum of the measures of the interior angles of a convex octagon. SOLUTION An octagon has 8 sides. Use the Polygon Interior Angles Theorem. (n 2) 180 = (8 2) 180 Substitute 8 for n. = Subtract. = 1080 Multiply. The sum of the measures of the interior angles of an octagon is 1080.
4 EXAMPLE Warm-Up 2Exercises Find the number of sides of a polygon The sum of the measures of the interior angles of a convex polygon is 900. Classify the polygon by the number of sides. SOLUTION Use the Polygon Interior Angles Theorem to write an equation involving the number of sides n. Then solve the equation to find the number of sides. (n 2) 180 = 900 n 2 = 5 n = 7 Polygon Interior Angles Theorem Divide each side by 180. Add 2 to each side. The polygon has 7 sides. It is a heptagon.
5 Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 1. The coin shown is in the shape of a regular 11- gon. Find the sum of the measures of the interior angles The sum of the measures of the interior angles of a convex polygon is Classify the polygon by the number of sides. decagon
6 EXAMPLE Warm-Up 3Exercises Find an unknown interior angle measure ALGEBRA Find the value of x in the diagram shown. SOLUTION The polygon is a quadrilateral. Use the Corollary to the Polygon Interior Angles Theorem to write an equation involving x. Then solve the equation. x = 360 x = 360 x = 72 The value of x is 72. Corollary to the Polygon Interior Angles Theorem Combine like terms. Subtract 288 from each side.
7 Warm-Up Exercises GUIDED PRACTICE for Example 3 3. Use the diagram at the right. Find m S and m T. 103, The measures of three of the interior angles of a quadrilateral are 89, 110, and 46. Find the measure of the fourth interior angle. 115
8 EXAMPLE Warm-Up 4Exercises Standardized Test Practice SOLUTION Use the Polygon Exterior Angles Theorem to write and solve an equation. x + 2x = 360 Polygon Exterior Angles Theorem 3x = 360 x = 68 Combine like terms. Solve for x. The correct answer is B.
9 Warm-Up Exercises GUIDED PRACTICE for Example 4 5. A convex hexagon has exterior angles with measures 34, 49, 58, 67, and 75. What is the measure of an exterior angle at the sixth vertex? 77
10 EXAMPLE Warm-Up 5Exercises Find angle measures in regular polygons TRAMPOLINE The trampoline shown is shaped like a regular dodecagon. Find (a) the measure of each interior angle and (b) the measure of each exterior angle. SOLUTION a. Use the Polygon Interior Angles Theorem to find the sum of the measures of the interior angles. (n 2) 180 = (12 2) 180 = 1800
11 EXAMPLE Warm-Up 5Exercises Find angle measures in regular polygons Then find the measure of one interior angle. A regular dodecagon has 12 congruent interior angles. Divide 1800 by 12: = 150. The measure of each interior angle in the dodecagon is 150.
12 EXAMPLE Warm-Up 5Exercises Find angle measures in regular polygons b. By the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles, one angle at each vertex, is 360. Divide 360 by 12 to find the measure of one of the 12 congruent exterior angles: = 30. The measure of each exterior angle in the dodecagon is 30.
13 Warm-Up Exercises GUIDED PRACTICE for Example 5 6. An interior angle and an adjacent exterior angle of a polygon form a linear pair. How can you use this fact as another method to find the exterior angle measure in Example 5? Linear pairs are supplementary. Since the interior angle measures 150, the exterior angle must measure 30.
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Unit 3: Triangles and Polygons Background for Standard G.CO.9: Prove theorems about triangles. Objective: By the end of class, I should Example 1: Trapezoid on the coordinate plane below has the following
Angle Unit Definitions
ngle Unit Definitions Name lock Date Term Definition Notes Sketch D djacent ngles Two coplanar angles with a coon side, a coon vertex, and no coon interior points. Must be named with 3 letters OR numbers