Types of Angles TC2MA234

Definition: An Angle is the union of two rays that share an end-point. The rays of the angles are the sides of the angle. The common end-point is called the vertex.

Denoting angles The following angle is denote as ∠ABC A B C

Protractor A protractor is used to measure an angle in degrees.

Worksheet: Measuring angles using a protractor.

Angles There are Six types of angles Right angle Straight angle Acute angle Obtuse angle Reflex Angle Full Rotation

Right Angles Forms a square corner Forms a 90 degree angle. 90 degrees

RIGHT ANGLES measure exactly 90 ° The “square” symbol means 90’

Straight Angle Forms a straight line Angle is 180 degrees 180 degrees

STRAIGHT ANGLE is exactly 180 ° A straight angle is 180 degrees This is a straight angle

Worksheet Straight angles.

Acute Angles Forms an angle that is less than a right angle Angle is less than 90 degrees

ACUTE ANGLES are less than 90°

Obtuse Angles Form an angle that is more than a right angle Angle is more than 90 degrees

OBTUSE ANGLES are greater than 90 ° but less than 180 °

FULL ROTATION A full rotation is 360 degrees The angle around a point is 3600

Reflex Angle A Reflex Angle is more than 180° but less than 360° This is a reflex angle

Worksheet Angles around a point.

CONGRUENT CONGRUENT means identical in form/same shape and size. CONGRUENT LINE SEGMENTS means two line segments are of equal length. CONGRUENT Angles means two angles are of equal measure. ● ● ● ●

Theorems If two angles are right, then they are congruent.

Angle Bisector A ray that divides an angle into 2 congruent adjacent angles. BD is an angle bisector of <ABC. A D B C

Ex: If FH bisects EFG & mEFG=120o, what is mEFH?

Solve for x, given that BD bisects ∠ABC. * If they are congruent, set them equal to each other, then solve! D A x+40o x+40 = 3x-20 40 = 2x-20 60 = 2x 30 = x 3x-20o C B

Supplementary, and Complementary Angles

Adjacent angles Adjacent angles are angles that share the same vertex and a common side. 15º 45º

These are examples of adjacent angles. 45º 80º 35º 55º 130º 50º 85º 20º

These angles are NOT adjacent. 100º 50º 35º 35º 55º 45º

Supplementary angles add up to 180º. 40º 120º 60º 140º Adjacent and Supplementary Angles Supplementary Angles but not Adjacent

Supplementary Angles - Two angles whose measures add up to 180 degrees Supplementary Angles - Two angles whose measures add up to 180 degrees. Supplementary angles can be placed so that they form a straight line. Example: angle A = 80 degrees and angle B = 100 degrees. Then angle A + angle B = 180 degrees. We can say that angles A and B are supplementary.

Complementary angles add up to 90º. 30º 40º 50º 60º Adjacent and Complementary Angles Complementary Angles but not Adjacent

Complementary Angles - Two angles whose measures add up to 90 degrees. Example: angle A = 30 degrees and and angle B = 60 degrees. Then angle A + angle B = 90 degrees. We can say angles A and B are complementary.

Example: If ∠AOC is a right angle, and m ∠AOB is 85o find m ∠BOC.

Example: Solve for x

Exercise: Find the measure of an angle if its measure is 24 degrees more than the measure of its complement.

Theorem: If two angles are complements of the same angle, then they are congruent. If two angles are congruent, then their complements are congruent.

Don’t change your radius! Construction #1 Construct a segment congruent to a given segment. This is our compass. Given: A B Procedure: 1. Use a straightedge to draw a line. Call it l. Construct: XY = AB 2. Choose any point on l and label it X. Don’t change your radius! 3. Set your compass for radius AB and make a mark on the line where B lies. Then, move your compass to line l and set your pointer on X. Make a mark on the line and label it Y. l X Y

Construct an angle congruent to a given angle Construction #2 Construct an angle congruent to a given angle Procedure: A C B Given: 1) Draw a ray. Label it RY. D 2) Using B as center and any radius, draw an arc intersecting BA and BC. Label the points of intersection D and E. E Construct: 3) Using R as center and the SAME RADIUS as in Step 2, draw an arc intersecting RY. Label point E2 the point where the arc intersects RY D2 4) Measure the arc from D to E. R Y 5) Move the pointer to E2 and make an arc that that intersects the blue arc to get point D2 E2 6) Draw a ray from R through D2

Bisector of a given angle? Construction #3 How do I construct a Bisector of a given angle? C A B Z Given: X Y Procedure: Using B as center and any radius, draw and arc that intersects BA at X and BC at point Y. 2. Using X as center and a suitable radius, draw and arc. Using Y as center and the same radius, draw an arc that intersects the arc with center X at point Z. 3. Draw BZ.