Angle Relationships Day 1

Angles angle sides vertexAn angle consists of two different rays (sides) that share a common endpoint (vertex). Sides Vertex

There are several ways to name an angle. 1) Use the vertex and a point from each side. SRT or TRS The vertex letter is always in the middle. 2) Use the vertex only. R 3) Use a number. 1 R S T vertex side 1 This only works if there is only one angle at a vertex.

B A 1 C 1) Name the angle in four ways. ABC 1 B CBA 2) Identify the vertex and sides of this angle. Point B BA andBC vertex: sides:

W Y X 1) Name all angles having W as their vertex. 1 2 Z 1 2 2) What are other names for ? 1 XWY or YWX 3) Is there an angle that can be named ? W No! XWZ ZWX ZWYYWZ XWY YWX

Vocabulary congruent vertical angles adjacent angles complementary angles supplementary angles

1 2 To show that  1 is congruent to  2, we use arcs. Z X To show that there is a second set of congruent angles,  X and  Z, we use double arcs. X  ZX  Z This “arc” notation says that: When two angles are congruent they have the SAME measure. This “arc” notation says that: 1  21  2

When 2 lines intersect, they make vertical angles

Vertical angles are opposite one another and are congruent  1   3  2   4

Find the value of x in the figure: The angles are vertical angles. So, the value of x is 130°. 130° x°

Find the value of x in the figure: The angles are vertical angles. (x – 10) = 125 (x – 10)° 125° x – 10 = 125 x = 135°

Adjacent angles are angles that: M J N R 1 2  1 and  2 are adjacent with the same vertex R and a common side A) share a common side, and B) have the same vertex Adjacent angles are “side-by-side”

Determine whether  1 and  2 are adjacent angles. No. They have no common side. 1 2 B 1 2 G Yes. They are “side-by-side”. N 1 2 J L No. They do not have a common vertex or a common side. The side of  1 is The side of  2 is

Complementary Angles  Complementary angles are two angles that form a right angle and whose measures have a sum of 90 degrees.  Complementary angles can be adjacent or nonadjacent Remember: The box in the corner means it’s a right angle.

Examples 65º 25º These are examples of complementary angles. 60º30º 65° + 25° = 90°30° + 60° = 90°

x H 75° I The angles below are complementary angles. Find the missing angle measure. m  H + m  I = 90° x + 75 = x = 15° m  PHQ + m  QHS = 90° x + 50 = x = 40° 50° H x Q P S

Supplementary Angles  Supplementary angles are two angles that form a straight line and whose measures have a sum of 180 degrees.  Supplementary angles can be adjacent or nonadjacent

Examples These are examples of supplementary angles. 120° + 60° = 180° 135° + 45° = 180° 60º 120º 45º135º

x H 75° I m  H + m  I = 180° x + 75 = x = 105° m  PHQ + m  QHS = 180° x = x = 50° x H 130° Q P S The angles below are supplementary angles. Find the missing angle measure.

Find each unknown angle measure. x + y + 80° = 180° –80° x + y = 100° The sum of the measures is 180°. x and y are congruent. x = 50° and y = 50° Each angle measures half of 100°. x 80° K M L NJ y Example:

Find each unknown angle measure. x + y + 50° = 180° –50° x + y = 130° The sum of the measures is 180°. ABC and DBE are congruent. x = 65° and y = 65° Each angle measures half of 130°. x 50° B DC EA y You Try:

20° C J D E F G H = 70° = 90° 70°= = 20° 90°= Box in the corner indicates a right angle. Find the missing angle measures given that m<u = 20°. v w x y z <u and <v are complementary angles, so v + 20 = v = 70° <w and <ECG are supplementary angles, so w + 90 = w = 90° <v and <y are vertical angles so y = 70° <u and <x are vertical angles so x = 20° u <w and <z are vertical angles so z = 90°

Practice: Angle Relationships Packet