Understanding Exterior Angles in Polygons

Slide Note

This content explains the concept of exterior angles in polygons and the Exterior Angle Theorem. It covers how exterior angles are formed when the sides of a polygon are extended, their relationship with interior angles, and how to calculate their measures using the Exterior Angle Theorem. Various examples are provided to demonstrate the application of the theorem in solving for unknown angle measures.

denise Follow

Uploaded on Jul 31, 2024 | 2 Views

Download Presentation

Please find below an Image/Link to download the presentation.

The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.

E N D

Presentation Transcript

EXTERIOR ANGLES

Angles When the sides of a polygon are extended, other angles are formed. The original angles are the interior angles. The angles that form linear pairs with the interior angles are the exterior angles.

EXTERIOR ANGLE THEOREM An exterior angle of a triangle is equal in measure to the sum measures of its two remote interior angles. sum of the remote remote interior interior angles angles Exterior angle Exterior angle

EXTERIOR ANGLE THEOREM (YOUR NEW BEST FRIEND) The measure of an exterior angle in a triangle is the sum sum of the measures of the 2 remote interior remote interior angles exterior exterior angle angle remote remote interior interior angles angles 2 2 1 1 3 3 4 4 m<1 + m<2 = m<4 m<1 + m<2 = m<4

EXTERIOR ANGLE THEOREM m 1 = m A + m B

EXAMPLES m<FHG = 180 111 = 69 linear pair m<G = 60 + 69

EXAMPLES Find x & y y = 30 + 82 y = 112 82 30 x y 180 = 30 + 82 + x 180 = 112 + x 68 = x x = 68 y = 112

EXAMPLES Find m JKM 2x 5 = x + 70 x 5 = 70 x = 75 m< JKM = 2(75) - 5 m< JKM = 150 - 5 m< JKM = 145

EXAMPLES Solve for y in the diagram. Solve on your own Solve on your own before viewing the before viewing the Solution

SOLUTION 4y + 35 = 56 + y 3y + 35 = 56 3y = 21 y= 27 y= 27

EXAMPLES Find the measure of in the diagram shown. 1 Solve on your own Solve on your own before viewing the before viewing the Solution

SOLUTION 40 + 3x = 5x - 10 40 = 2x - 10 50 = 2x 25 = x 25 = x m < 1= 5x - 10 m < 1= 5(25) - 10 m < 1= 125 - 10 m m < 1= 115 < 1= 115

CHECKPOINT: COMPLETE THE EXERCISES.

SOLUTION x + 70 = 3x + 10 70 = 2x + 10 60 = 2x 30 = x Right Scalene triangle 3 (30) + 10 = 100

TRIANGLE INEQUALITIES

Make A Triangle Construct triangle DEF. D E D F F E

Make A Triangle Construct triangle DEF. D E D F F E

Make A Triangle Construct triangle DEF. D E

Make A Triangle Construct triangle DEF. D E

Make A Triangle Construct triangle DEF. D E

Make A Triangle Construct triangle DEF. 5 3 D E 13 Q: What s the problem with this? A: The shorter segments can t reach each other to complete the triangle. They don t add up.

Triangle Inequality Conjecture The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Add the two smallest sides; they MUST be larger than the third side larger than the third side for the triangle to be formed.

Make A Triangle Can the following lengths form a triangle? 2.2 ft 2 ft 9 ft 9 ft 13 ft 13 ft 1.4 mm 4 mm 5 mm 5 mm 10 mm 10 mm 3.5 cm 5 cm cm 4 cm 4 cm 4.7 7 ft ft 15 15 ft ft ft ft ?? cm ? 6.7 7 ft ft 7 7 ft ft ft ft 5.10 mm 10 mm 3 mm 3 mm 6 mm 6 mm 7.10 mm 10 mm 13 mm 13 mm mm mm ? 8.8 m 8 m 7 m 7 m 1 m 1 m ? 10. 12. 9. 11. 1 mm 1 mm 5 mm 5 mm 3 mm 3 mm 9 mm 9 mm 2 mm 2 mm 1 mm 1 mm 12 mm 12 mm 22 mm 22 mm mm mm ?? 7 mm 7 mm 8 mm 8 mm mm mm ??