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Lesson 11-1 Angle and Line Relationships Adjacent Angles – two angles that share a common side with the same vertex Vertical Angles – two angles formed when two lines intersect and the angles are non-adjacent to each other Complementary Angles – the sum of the measure of two angles equals 90 degrees Supplementary Angles – the sum of the measure of two angles equals 90 degrees Real-World Example 1 Find a Missing Angle Measure CARPENTRY Mark cuts through the corner of a rectangular 63 board at a 63 angle. x a. Classify the relationship between the 63 angle and x. The angles at the cut point are complementary. b. What is the measure of x? Since the angles are complementary, the sum of their measures is 90°. mx + 63 = 90 mx + 63 – 63 = 90 – 63 mx = 27 Write the equation. Subtract 63 from each side. Simplify. So, mx = 27. Perpendicular Lines – two lines that form right angles Parallel Lines – two lines in a plane that never intersect Transversal – a line that intersects two or more other lines in a plane Alternate Interior Angles – two angles between parallel lines that are on opposite sides of the transversal (Note: they must involve using all three lines) Alternate Exterior Angles – two angles outside the parallel lines that are on opposite sides of the transversal (Note: they must involve using all three lines) Corresponding Angles – two angles on the same side of the transversal but one is interior and the other is exterior (Note: they must involve using all three lines) Example 2 Find Measures of Angles Formed by Parallel Lines In the figure at the right, m || n and t is a transversal. a. Classify the relationship between 6 and 1 and the relationship between 1 and 5. 6 and 1 are alternate exterior angles. 1 and 5 are corresponding angles. b. If m6 = 55, find m1 and m5. Since 6 and 1 are alternate exterior angles, they are congruent. So, m1 = m6 = 55. Since 1 and 5 are corresponding angles, they are congruent. So, m5 = m1 = 55. Example 3 Use Algebra to Find Missing Angle Measures ALGEBRA Angles DEF and GHI are supplementary. If mDEF = x – 6 and mGHI = 2x + 9, find the measure of each angle. Step 1 Find the value of x. mDEF + mGHI = 180 (x – 6) + (2x + 9) = 180 3x + 3 = 180 3x = 177 x = 59 Step 2 Supplementary angles Substitution Combine like terms. Subtract 3 from each side. Divide each side by 3. Replace x with 59 to find the measure of each angle. mDEF = x – 6 = 59 – 6 or 53 So, mDEF = 53 and mGHI = 127. mGHI = 2x + 9 = 2(59) + 9 or 127