Angle 3 and angle ABChave a common interior space

a common vertex andNo common interior

Angle 3 and angle ABC do nothave 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 2are across from eachother.

Angle 3 and angle 4are also across from eachother.

Although angles AEB and DEC are across from each other, they do not create a perfectly straight X.

a) ROADWAYS Name an angle pair that satisfies the condition two angles that form a linear pair.

SAMPLE ANSWER:

PIQ and QIS

b) ROADWAYS Name an angle pair that satisfies the condition two acute vertical angles.

SAMPLE ANSWER:

PIQ and TIS

(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!)

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 = 1805x - 6 + x = 180

6x - 6 = 1806x = 186x = 31x represents “the other angle”, so 2 = 31 1 = 5x-6 = 5(31) – 6 = 149 so 1 = 149

Even though only one symbol is drawn,There are 4 right angles.

(four 90 angles)

“Line AD is perpendicular to line CB.”

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 mMJO = 3y + 6,set up the following equation:3y + 6 = 90. Solve for y.3y = 84y = 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 + 6+ 9x = 90. Solve for x.12x + 6 = 9012x = 84x = 7

Important to READ through.

NEVER assume anything in apicture is congruent or perpendicular. It must be told to you in directions,or already marked in the picture.

Determine whether the following statement can be justified from the figure below. Explain.

a) mVYT = 90°

Yes. This is true because XYVis marked as a right angle and createsa linear pair with TYV.Linear pairs add to 180. If one angle is 90then the other angle must also be 90.

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 anglesform a linear pair. Linear pairs add to 180.Supplementary angles also add to 180.

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.