C A D B mÐABC = 14x + 2, mÐCBD = 6x + 1, mÐABD = 25x – 27

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Presentation transcript:

C A D B mÐABC = 14x + 2, mÐCBD = 6x + 1, mÐABD = 25x – 27 Find x, mÐABC, mÐCBD, and mÐABD WARMUP - A C D mÐABC = 14x + 2 B mÐABC = 14(6) + 2 = 86 mÐABC + mÐCBD = mÐABD mÐCBD = 6x + 1 14x + 2 + 6x + 1 = 25x – 27 mÐCBD = 6(6) + 1 = 37 20x + 3 = 25x – 27 3 = 5x – 27 mÐABD = 25x - 27 30 = 5x mÐABD = 25(6) - 27 = 113 6 = x x = 6 mÐABC = 86° mÐCBD = 37 ° mÐABD = 113 °

What are some special angle relationships? Agenda: Warmup Review angles from yesterday Special angle pairs

Complementary Angles Definition: two angles whose measures have the sum of 90°. 35° 55° 20° 70° Complementary Angles may or may not be Adjacent Angles.

Supplementary Angles Definition: two angles whose measures have the sum of 180°. 110° 70° 125° 55° Supplementary Angles may or may not be Adjacent Angles.

Definition: two supplementary, adjacent angles. Linear Pair Definition: two supplementary, adjacent angles. 120° 60° Linear Pair = A Pair of Angles that forms a Line.

Definition: two non-adjacent angles formed by intersecting lines. Vertical Angles Definition: two non-adjacent angles formed by intersecting lines. 1 2 3 4 Ð1 and Ð2 are vertical angles. Ð3 and Ð4 are vertical angles.

1 4 3 2 Ð3@Ð4 Ð1@Ð2 What do you notice? Theorem: Vertical Angles are Congruent.

10x - 18 8x + 6 102 Find x. Applying new concepts with Algebra… C A Q We know vertical angles are congruent; therefore the measure of vertical angles are equal and we can set these two expressions equal to one another. 10x – 18 = 8x + 6 2x = 24 x = 12

18° x + 4x = 90° 5x = 90° 72° x = 18 What relationship do we see here? Complementary Angles 18° 72° x + 4x = 90° x° 4x° 5x = 90° x = 18

Supplementary Angles 109° 71° 4x+3 6x+7 4x+3 + 6x+7 = 180° x = 17 10x + 10 = 180 10x = 170

CHECK FOR UNDERSTANDING P. 71 #15, 16, 20, 21 P. 72 #37 P. 79 #28, 29 P 80 #54, 55