Interior and Exterior Angles of Triangles. Right Angle A right angle has a measurement of 90...
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Transcript of Interior and Exterior Angles of Triangles. Right Angle A right angle has a measurement of 90...
Interior and Exterior Angles of Triangles
Right Angle
A right angle has a measurement of 90 degrees90
Straight Angle
180A straight angleHas a measurementOf 180 degrees
Acute Angle
An acute angle hasA measurement ofLess than 90 degrees
Obtuse Angle
An obtuse angle hasA measurement ofMore than 90 degrees
Complimentary Angles
• Their measures add up to exactly 90 degrees
60
30
Supplementary Angles
• Their measures add up to exactly 180 degrees
60120
Finding Missing Angles
25º
x
x + 25 = 90
45º xx + 45 = 180
Finding the complimentary and supplementary angles
30° Complimentary: 30 + x = 90Supplementary: 30 + x = 180
The complimentary angle is 60⁰ and the supplementary angle is 150⁰
65°
The complimentary angle is ___⁰ and the supplementary angle is _____⁰
105°
In this case there is no complimentary angle, only a supplementary angle. Why?
Triangles
Finding a Missing Angle
• The sum of all angles in a triangle is 180 degrees.
• You should remember that from last year, but why?
Let’s Look at it Three Ways
• Cutting off the angles
1
2
31
2
3
I cut off angles 2 and 3 and lined them up to form a straight line
Rotating the Triangle
1
2
3
1
2
3
3 1
2
In this picture angles 1, 2, and 3 combine to make a straight line of 180⁰
Using parallel lines and transversals
1
2
3
2 31
Angle 2 by vertical angles, angles 1 and 3 by complimentary angles
Putting it into action
85
60
x
180 60 85 x 180 145 x
35 x
Your Turn
60 65
x
Finding an exterior angle-Create a straight line to solve
45 80
55
x
180 80 x
100x
80⁰ + x⁰ make up the straight line. The 55⁰ and 45⁰ have nothing to do with it.
Your Turn
x
35°
55°
60º
60º
60º x
145ºx
y
Find all the missing angles
85° 154°
Closure
• Two angles that are supplementary add up to ______
Closure
• Two angles that are complimentary add up to ______
Closure
• A straight line is _______
Closure
• The sum of all angles in a triangle equals:
Closure: With a partner find all the missing angles
125° 168°