Exterior Angle Theorem

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Presentation transcript:

Exterior Angle Theorem

How do we find the measurement of angle GFK?

We know that according to “triangle angle sums” angle GFH is 64° (180 – 116). We also know that angles GFH and GFK are supplementary , and supplementary angles add up to 180° Therefore, angle GFK must be 116° (180 – 64)

Find the measurement of angle ZAB 1. Angle BAC is 70° (180 – 110) according to triangle angle sums. Angles BAC and ZAB are supplementary angles so they must add up to 180° Therefore, angle ZAB is 110° (180 – 70)

From the two examples do you notice a pattern??? You should notice that the exterior angle of the triangle is equal to the sum of the 2 non-adjacent interior angles of the triangle. This is called the Exterior Angle Theorem

Example The measurement of angle CDE is equal to the sum of the measurements of angles EFD and DFE Therefore, the measurement of angle CDE is 123° (37 + 86)

For You To Try What is the measurement of angle HQR? Solution: 126° (56 + 70)

Using Algebra and the Exterior Angle Theorem Solution: 2x + 6x = 80 8x = 80 8 8 x = 10 6x = 6(10) = 60°

Another Example Solution: 12x – 4 + 30 = 16x – 2 12x + 26 = 16x – 2 -12x -12x 26 = 4x – 2 + 2 + 2 28 = 4x 4 4 7 = x 12x – 4 = 12(7) – 4 = 84 – 4 = 80°

For You To Try Solution: x + 18 + 40 = 6x – 2 x + 58 = 6x – 2 -- x - x + 2 + 2 60 = 5x 5 5 12 = x x + 18 = 12 + 18 = 30°