Angles: Setting up Equations

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Presentation transcript:

Angles: Setting up Equations

Right Angles Complementary angles: Set equation equal to 90. 3x+7 Add the two expressions. (3x + 7) + (4x +13) = 90 7x + 20 = 90 -20 -20 7x = 70 x = 10 Combine like terms: 7x + 20 = 90 Solve for x:

Perpendicular Lines A AB __BC ABD = 7x+2 DBC = 5x+4 D 7x+2 5x+4 B C Same as Complementary: adds to 90 degrees. AB __BC ABD = 7x+2 DBC = 5x+4 Set up the equation: 7x+2 + 5x+4 = 90 Combine Like Terms: 12x +6 = 90 Solve. D 7x+2 5x+4 B C

Supplementary Angles Supplementary Angles are along a straight line. Add to 180 degrees. 5x+7 3x+13 Set up: 5x+7 + 3x+13= 180 Combine: 8x +20 =180 Solve: -20 -20 Divide: 8x = 160 x = 20

Vertical Angles With vertical angles, the ones across from each other are equal. E D 9x-4 7x+10 B 9x - 4 = 7x +10 A C Variables on different sides of the equation. 9x – 4 = 7x + 10 -7x -7x 2x – 4 = 10 +4 +4 2x = 14 x= 7