User:JackyLeslie

Angle Pair Relationships *This page is a work in progress!


 * Adjacent Angles are non-overlapping angles that share a common side and a common vertex.

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 * Complementary Angles have measures that add to exactly 90 degrees.

Examples:

Question #1: If angles A and B are complementary and angle A is 43 degrees, what is the measure of angle B? Solution: Angle A and B must add to exactly 90 degrees, because they are complementary angles. So, angle B + 43 = 90. Subtract 43 from both sides of the equation: angle B + 43 - 43 = 90 - 43. Therefore, angle B must equal 47 degrees.

Question #2: Angles A and B are complementary angles. If angle A equals 2x + 4 and angle B equals x - 1, what is the value of x?

Solution: Angle A and B must add to exactly 90 degrees, because they are complementary angles. So, (2x + 4) + (x - 1) = 90 Combine like terms (2x and x; 4 and -1) results in: 3x + 3 = 90. Subtract 3 from both sides of the equation: 3x + 3 - 3 = 90 - 3 So, 3x = 87. Then, divide both sides by 3. Therefore, x = 29. *Note: The question only asked for the value of x, but we could also use this to find the measures of each angle if needed!

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 * Supplementary Angles have measures that add to exactly 180 degrees.

Question #1: If angles C and D are supplementary and angle C is 101 degrees, what is the measure of angle D?

Solution: Angle C and D must add to exactly 180 degrees, because they are supplementary angles. So, angle D + 101 = 180. Subtract 101 from both sides: angle D + 101 - 101 = 180 - 101 Therefore, Angle D = 79 degrees.

Question #2: Angles C and D are supplementary. If angle C equals 5x and angle D equals 3x + 12, what is the value of angle C?

Solution: Angle C and D must add to exactly 180 degrees, because they are supplementary angles. So, (5x) + (3x + 12) = 180. Combine like terms (5x and 3x) results in: 8x + 12 = 180. Subtract 12 from both sides of the equation: 8x + 12 - 12 = 180 - 12 So, 8x = 168. Then, divide both sides by 8. Therefore, x = 21. *Note: The question only asked for the value of x, but we could also use this to find the measures of each angle if needed!

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 * Vertical Angles are formed by intersecting lines and are opposite each other. They are congruent.

Question #1: If angles X and Y are vertical angles and angle X is 76 degrees, what is the measure of angle Y?

Solution: Angles X and Y are congruent, because they are vertical angles. So, angle Y must also be 76 degrees.

Question #2: One pair of vertical angles measures 5x - 1 degrees, and the other measures 4x +10 degrees. What is the value of x, and what is the value of each angle?

Solution: The two angles described must be congruent, because they are vertical angles. So, 5x - 1 = 4x + 10. Combine like terms by moving variables to one side of the equations and constants to the other. 5x - 1 = 4x + 10 + 1     + 1     ________________      5x = 4x + 11 - 4x - 4x _________________ Therefore, x = 11. DO NOT forget to finish the problem! The problem asks for the value of x, but it also wants the measure of each angle. So, you must remember to plug the value of x into one of the two expressions.

If 5x - 1 represents one of the two angles, when plugging in you get: 5(11) - 1 = 55 - 1 = 54 degrees.