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Opposite Rays Opposite Rays –Rays that are part of the same line and have only their
endpoint in common
Also called straight angle
XZXY and
Angle Another case when two rays share an endpoint… Angle –A figure formed by two noncollinear rays that have a
common endpoint Vertex – common endpoint Sides – rays that make up angle
Three ways to name: Three points (vertex in middle)
Vertex only
A number
Interior/Exterior Angle separates a plane into three regions Interior of the angle Exterior of the angleAngle itself
Angle Measure Degree –Unit that angles are measured in 1/360th of a circle Symbol: °
reads ‘the measure of angle PQR’ Reason why there is no degree sign, because it is a measure
and not a measurement
PQRm
Postulate 3-2: Protractor Postulate
Meaning: from a given ray, there are two ways to draw an angle with a given angle measure
Example Use a protractor to draw an angle having a
measure of 35.
Use a protractor to draw an angle having a measure of 65.
Classifying Angles Types of Angles:Right Angle – measure is 90
Acute Angle – measure is less than 90
Obtuse Angle – measure is more than 90
Example Find m∠ABC if
m∠ABD = 70 and m∠DBC = 43.
If m∠EBC = 55 and m∠EBD = 20, find m∠2.
Find m∠ABD if m∠ABC = 110 and m∠2 = 36.
Name the angle that forms a linear pair with ∠TCM.
Do ∠1 and ∠TCE form a linear pair? Justify your answer.
Example
Example The John Hancock Center in Chicago, Illinois,
contains many types of angles. Describe the highlighted angles.
Example Name a pair of nonadjacent supplementary
angles.
Find the measure of an angle that is supplementary to angle BGC.
Example Angles C and D are supplementary. If m∠C =
12x and m∠D = 4(x + 5), find x. Then find m∠C and m∠D.
Example Suppose ∠A ≅ ∠B
and m∠B = 47. Find the measure of an angle that is supplementary to ∠A.
In the figure below, ∠1 is supplementary to ∠2, ∠3 is supplementary to ∠2, and m2∠ = 105. Find m∠1 and m∠3.