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Concept Angle 3 and angle ABC have a common interior space a common vertex and No common interior Angle 3 and angle ABC do not have a common vertex. Non common sides form a straight line Non common sides do not form a straight line Think “2 sides that form a straight line” Think “2 angles that are next to eachother with a common side” If they can’t be adjacent, think “across from each other”. Diagram will always form a perfect X shape. Angle 1 and angle 2 are across from eachother. Angle 3 and angle 4 are also across from eachother. Although angles AEB and DEC are across from each other, they do not create a perfectly straight X.

Example 1 a) ROADWAYS Name an angle pair that satisfies the condition two angles that form a linear pair. SAMPLE ANSWER:  PIQ and  QIS

Example 1 b) ROADWAYS Name an angle pair that satisfies the condition two acute vertical angles. SAMPLE ANSWER:  PIQ and  TIS

Concept (always the same measure) (they can be adjacent angles or non adjacent angles) (they can be adjacent angles or non adjacent angles. If they are adjacent, then they are also a linear pair.) (like angle addition!)

Example 2 ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle. Watch and COPY: Supplementary means the measure of two angles will add up to 180 . Since we don’t know what “the other angle” is, let’s call it x. Then the first angle is 5x – 6 (six less (subtract) than 5 times (multiply) the other (x)) Use angle addition:  1 +  2 = 180 5x x = 180 6x - 6 = 180 6x = 186 x = 31 x represents “the other angle”, so  2 = 31   1 = 5x-6 = 5(31) – 6 = 149 so  1 = 149 

Concept Even though only one symbol is drawn, There are 4 right angles. (four 90  angles) “Line AD is perpendicular to line CB.”

Example 3 Find x and y so that KO and HM are perpendicular. If the lines are , a right  is formed.  MJO is a right angle. Right angles equal 90 . Since m  MJO = 3y + 6, set up the following equation: 3y + 6 = 90. Solve for y. 3y = 84 y = 28. To solve for x: Another right  is formed. Look at the angles that involve an x.  KJH is a right angle, but is created by adding 2 angles together.  KJI +  IJH =  KJH Substitute in to set up the following equation: 3x x = 90. Solve for x. 12x + 6 = 90 12x = 84 x = 7

Concept Important to READ through. NEVER assume anything in a picture is congruent or perpendicular. It must be told to you in directions, or already marked in the picture.

Example 4 Determine whether the following statement can be justified from the figure below. Explain. a) m  VYT = 90 ° Yes. This is true because  XYV is marked as a right angle and creates a linear pair with  TYV. Linear pairs add to 180. If one angle is 90  then the other angle must also be 90 .

Example 4 Determine whether the following statement can be justified from the figure below. Explain. b)  TYW and  TYU are supplementary. Yes. This is true because the two given angles form a linear pair. Linear pairs add to 180 . Supplementary angles also add to 180 .

Example 4 Determine whether the following statement can be justified from the figure below. Explain. c)  VYW and  TYS are adjacent angles. No. Although they share a common vertex, these angles do not share a common side.