Transcript Exploring Angles - Nutley Public Schools

Section 1.6a
Exploring Angles
< is the less than symbol
∠ is the angle symbol
Warm Up
1. Draw AB and AC, where A, B, and C are
noncollinear.
2. Draw opposite rays DE and DF.
Solve each equation.
3. 2x + 3 + x – 4 + 3x – 5 = 180
4. 5x + 2 = 8x – 10
 A ray is part of a line that extends indefinitely in one direction.
 It has exactly one endpoint and that point is named first when
naming the ray.
Ray AB or
Two rays create an angle.
The rays become the sides of the angle.
 If two rays form a line, they are called opposite rays.
A. What are the opposite rays?
B. What kind of angle do they form?
C. How many degrees is this angle?
Other angles are formed by two non-collinear rays with a
common endpoint called a vertex.
 What are the sides of this angle?
 What is the vertex?
 How do you name this angle?
When naming an angle, use 3 letters in which the vertex MUST be the middle
letter or you can name it by the number inside the angle.
 You can also name an angle by its vertex ONLY if the vertex represents one
single angle.
 How many angles do you see?
 What are they?
Write the different
ways you can name the
angles in the diagram.
Classifying angles:
But less than 180
Greater than
180 ̊ but
less than
360
 An angle separates a plane into 3 parts, the interior of the angle, the exterior
and the angle itself.
 Angles are measured in units called ___________.
 What tool is used to measure a segment?
 What tool is used to measure an angle?
 What other names can be used to identify ∠BCD?
 Name the vertex of ∠ 1.
 What are the sides of ∠ 2?
 Give other names for:
 ∠ RSQ
 ∠ QTR
 ∠ SUR
∠7
∠5
∠6
∠4 + ∠5 = ∠ ?
∠6 + ∠7 = ∠ ?
∠2 + ∠3 = ∠ ?
U
 Name 3 angles with vertex P.
 What 2 angles add up to 180 degrees?
 If ∠3 = 80 ̊ and ∠LPN = 100 ̊, Then m∠2 =
Find the measure of each angle. Then classify
each as acute, right, or obtuse.
A. WXV
B. ZXW
Use the diagram to find the measure of each
angle. Then classify each as acute, right, or
obtuse.
a. BOA
b. DOB
c. EOC