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Geometry Practice: Angle Measures and Polygons

Learn about angle measures in triangles and polygons, practice finding interior and exterior angles, and solve geometry problems with detailed explanations.

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Geometry Practice: Angle Measures and Polygons

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  1. Warm up x = y = 85° x 1. 65° 30° y 115° If <A in a triangle equals 70° what is the combined measure of <B and <C? 110° 3. If ΔXYZ has three congruent angles, what is the measure of <X? 60° 4. Find the measure of each angle. x = 5 30°, 55°, 95° (2x2 + 5) (3x2 + 2x + 10) (8x - 10)

  2. 3 1 180° 4 2 360° 5 3 540° 6 4 720° (Number of sides - 2 ) times 180° = sum of interior angles • Copy this table • Fill in the first column • Just using one vertex, draw as many diagonals as you can in each shape. • Fill in the middle column • How many degrees in a triangle? • Fill in the last column. • Look at this:

  3. The measure of INTERIOR ANGLESin a polygon In a polygon with n sides, the total measure of interior angles = 180(n – 2)

  4. The measure of EXTERIOR ANGLES in a polygon is always 360°

  5. Example: Find the measures of each interior and each exterior angle in the pentagon. You can start by finding the interior OR the exterior measures. This is a REGULAR pentagon. Find the INTERIOR measure first: 180(5-2) = 180(3) = 540° (total interior degrees) 540/5 = 108° Therefore the exterior is 72° Find the EXTERIOR measure first: 360/5 = 72° Therefore the interior is 108°

  6. Try this one Draw a regular octagon • Find the sum of the measures of the interior angles. • Find the measure of EACH interior angle. • Find the measure of EACH exterior angle. • 1080° • 135° • 45°

  7. 360° ≈32.73° ≈147.27° Another practice problem… Find the sum of the measures of the exterior angles in an 11-gon. IF the 11-gon was regular, what would be the measure of EACH exterior angle? What would be the measure of EACH interior angle?

  8. 115° 120° y° 54° x° z° 48° 100° The fish problem(put this in your notes) X = 78° Y = 102° Z = 127°

  9. Uno mas Find the measure of an interior angle and an exterior angle in a regular dodecagon Exterior 360/12 = 30° Interior 180° – 30° = 150°

  10. Assignment Pg 180, 9-40

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