Angle Relationships

Angles Angles have two sides that share a common endpoint called a vertex of the angle. Angles are most commonly measured in degrees – for example 90°, 175° VERTEX ANGLE SIDE

Classifying Angles – 4 types RIGHT ANGLE – an angle that is exactly 90° ACUTE ANGLE – an angle that is less than 90° OBTUSE ANGLE – an angle that is more than 90° STRAIGHT ANGLE – an angle that is exactly 180°

Naming Angles Sometimes angles use a single letter to name them Angle H Angle R Angle S

Naming Angles When there are many lines connected with many letters, then you name them by 3 letters.

Name the angles

Types of Angles Vertical Angles Adjacent Angles Complementary Angles Supplementary Angles

Vertical angles have the same measure. Angle 1 and 4 are vertical angles 1 ANGLES 2 AND 3 ARE CONGRUENT ANGLES Angles 2 and 3 are vertical angles 3 2 4 ANGLES 1 AND 4 ARE CONGRUENT ANGLES When two lines intersect, they form two pairs of opposite angles called VERTICAL ANGLES Vertical angles have the same measure. Angles with the same measure are called CONGRUENT ANGLES (equal)

The angle labeled x° and the angle labeled 140 are vertical angles. Find the value of x in the figure x° 140° 140° The angle labeled x° and the angle labeled 140 are vertical angles. Therefore, they are congruent. So, the value of x is 140°

Find the value of x in each figure 23° x° X = 95° 95°

ANGLES 1 AND 2 ARE ADJACENT ANGLES 3 2 4 When two lines intersect, they form two pairs of side by side angles called ADJACENT ANGLES Adjacent angles share one vertex and one side

Name acute adjacent angles B C D E F G Name adjacent angles Name acute angles Name acute adjacent angles Name obtuse angles

SUPPLEMENTARY ANGLES If the sum of 2 angles is 180°, then the angles are SUPPLEMENTARY 120° 60° 145° 35° 120° + 60° = 180° 145° + 35° = 180°

COMPLEMENTARY ANGLES If the sum of 2 angles is 90°, then the angles are COMPLEMENTARY 75° 30° 15° 60° 75° + 15° = 90° 30° + 60° = 90°

Classify as complementary, supplementary or neither

Complementary, Supplementary or Neither?

Finding the value of x in the figure This angle is 180° so 120 + x = 180 X = 60° This angle is 90° So 20 + x = 90 X = 70°

Find the value of x in each figure

Name complementary angles Name vertical angles Name supplementary angles What is the measure of angle BGC? What is the measure of angle CGD?

Name complementary angles What is the measure of x? What is the measure of angle CEA? What is the measure of angle AED? Name acute vertical angles Name obtuse vertical angles Name supplementary angles