25.	+Consecutive+Interior+Angle+Theorem


 * Consecutive Interior Angle Theorem**


 * Summary:** The consecutive interior angle theorem is when two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary. You can use this theorem to state, that when two angles, are both in the inside lines cut by a transversal, those two angles are supplementary.



In the picture above the consecutive interior angles are: Angles 3 & 5 Angles 4 & 6

• When finding the value of the two consecutive interior angles, you must note that they are supplementary thus they must add up to 180º • Both sides of the consecutive interior angles add up to 180º, however the lines need to be parallel for it to be 180º • Formula: (for the following example) In the picture above, 4 and 6 are consecutive interior angles. When the measures of angle 4 and angle 6 are added together then the final solution will equal 180. Therefore, when adding the two unknown measures together have them equal 180. (supplementary)
 * Rules, Properties, and Formulas:**

Examples:


 * A)**



A) Find the value of x, and find the measurements of angles 4 and 6. (in the picture above, note: figure is not drawn to scale) Measure of angle 4 = 2x + 8 Measure of angle 6 = 140

Explanation and Answer: 2x + 8 + 140 = 180 2x + 148 = 180 2x = 32 x = 16 • Plug in 16 for x and you find your angle measures.

x = 16 Measure of Angle 4 = 40 Measure of Angle 6 = 140


 * B)**

B) Find the value of y, and use that to find the measurements of the corresponding interior angles 5 and 3 (in the picture above, note: figure is not drawn to scale) Measure of Angle 5 = 3y + 8 Measure of Angle 4 = y - 4

Explanation and Answer: 3y + 8 + y - 4 = 180 4y - 4 = 180 4y = 176 y = 44 •Plug in 44 for y and you find your angle measures

y = 44 Measure of Angle 5 = 140 Measure of Angle 4 = 40

C) Find the value of a, and use that to find the measurements of the corresponding interior angles 3 and 6 (in the picture above, note: figure is not drawn to scale) Measure of Angle 3 = 42 + 14a Measure of Angle 6 = -8a + 12
 * C)**

Explanation and Answer: 42 + 14a - 8a + 12 = 180 54 + 6a = 180 6a = 126 a = 21 •Plug in 21 for a and you find your angle measures

a= 21 Measure of Angle 3 = 336 Measure of Angle 6 = -156

Helpful Hint for All Consecutive Interior Angles • Since consecutive interior angles are supplementary they always add up to 180 • Use the measurements given to you for both of your consecutive Interior Angles, and make the equal to 180 • Solve and you get your answer

[|Consecutive Interior Angle Theorem Explanation] [|Consecutive Interior Angle Definition] [|Consecutive Interior Angle Theorem Example Website]
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