Angle • Two rays with the same endpoint

•. The rays are the sides. of the angle. •. The common endpoint • The rays are the sides of the angle. • The common endpoint of the 2 rays is the vertex of the angle.

Name the sides and vertex of this angle:

Name the sides and vertex of this angle:

We sometimes refer to the interior and exterior of an angle.

What points lie  on the interior?  on the exterior?  on the angle?

You can name angles many different ways:

•. named with 1 letter, the letter. must be the vertex • • named with 1 letter, the letter must be the vertex • named with 3 letters, the middle letter is the vertex, and the others are 1 point on each ray

Give as many names as you can for these angles.

Give as many names as you can for these angles. DEF FED E

Give as many names as you can for these angles. TUV VUT U

We sometimes also name angles with numbers, particularly when there are several angles in the same picture. 5 is at the bottom left.

The measure of an angle refers to how wide the angle opens, NOT how long the sides are (because they go on forever) or which way it points.

There are many ways to measure angles There are many ways to measure angles. The oldest and most common unit of measurement is the degree.

• A full circle has 360o • A straight line has 180o

Types of Angles

•. Acute. •. less than 90o •. Right. •. exactly 90o. • • Acute • less than 90o • Right • exactly 90o • We often use a box to show an angle is a right angle.

•. Obtuse. •. between 90o and 180o •. Straight. •. exactly 180o. • • Obtuse • between 90o and 180o • Straight • exactly 180o • same as a line

The tool used to measure angles is called a protractor.

The tool used to measure angles is called a protractor.

Various types of protractors have been used for thousands of years, mostly in navigation and construction.

In modern practical applications, angles are measured by sighting laser beams.

We refer to the measure of an angle with notation that uses the letter “m”. mACD = 138 mB = 80

IMPORTANT: We don’t normally use protractors much in geometry IMPORTANT: We don’t normally use protractors much in geometry. This is because pictures are intended to give the idea of what’s going on, but they may not necessarily be accurate.

Congruent Angles Angles are congruent if and only if they have the same measure. R  Q

Congruent Angles

In drawings we show angles are congruent by marking the same arcs of a circle inside the angles.

Find mCAB.

64 – 53 = 11o Find mCAB.

mADC = 50 Find x Find m BDC

mADC = 50 Find x Find m BDC x + 7 + 2x + 19 = 50 3x + 26 = 50

mADC = 50 Find x Find m BDC 3x + 26 = 50 3x = 24  x = 8

mADC = 50 Find x Find m BDC m BDC = 2x + 19 2  8 + 19 = 16 + 19 = 35o

Remember … . Angle, side vertex, interior,. exterior  Remember …  Angle, side vertex, interior, exterior  Naming angles  Measuring angles, protractor, degree  Acute, obtuse, right, straight  Congruent angles