Download Angle Measures of Triangles

Extension
Angle Measures of Triangles
7.3
Lesson Tutorials
Sum of the Angle Measures of a Triangle
Algebra
EXAMPLE
yí
The sum of the angle measures
of a triangle is 180°.
Words
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x + y + z = 180
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Finding Angle Measures
1
Find each value of x. Then classify each triangle.
a.
COMMON
CORE
b.
xí
45í
Geometry
In this extension, you will
● understand that the sum of
the angle measures of any
triangle is 180°.
● find missing angle
measures in triangles.
Learning Standard
7.G.5
28í
50í
xí
x + 45 + 90 = 180
x + 28 + 50 = 180
x + 135 = 180
x + 78 = 180
x = 45
x = 102
The value of x is 45. The
triangle has a right angle
and two congruent sides.
So, it is a right isosceles
triangle.
The value of x is 102. The
triangle has one obtuse
angle and no congruent
sides. So, it is an obtuse
scalene triangle.
Find the value of x. Then classify the triangle.
2.
1.
45í
44í
3.
78î
53í
27î
xî
xí
xí
xí
4.
5.
xí
37í
6.
48í
73í
60í
13í
84í
xí
60í
Tell whether a triangle can have the given angle measures. If not, change the first angle
measure so that the angle measures form a triangle.
7. 76.2 °, 81.7 °, 22.1°
2
3
1
3
9. 5 — °, 64 — °, 87 °
288
Chapter 7
MSCC3_Red_PE_0703b.indd 288
8. 115.1°, 47.5 °, 93 °
3
4
1
2
3
4
10. 31 — °, 53 — °, 94 — °
Constructions and Scale Drawings
12/4/12 11:56:39 AM
EXAMPLE
Finding Angle Measures
2
Find each value of x. Then classify each triangle.
Math
Practice
a. Flag of Jamaica
b. Flag of Cuba
xî
Analyze Givens
xî
xî
128î
What information
is given in the
problem? How
can you use
this information
to answer the
question?
xî
60î
x + x + 128 = 180
x + x + 60 = 180
2x + 128 = 180
2x + 60 = 180
2x = 52
2x = 120
x = 26
x = 60
The value of x is 26. The
triangle has one obtuse
angle and two congruent
sides. So, it is an obtuse
isosceles triangle.
The value of x is 60.
All three angles are
congruent. So, it is
an equilateral and
equiangular triangle.
Find the value of x. Then classify the triangle.
11.
xî
12.
13.
132î
60î
xî
45î
xî
xî
14.
15.
(2x à 15)í
xî
xî
(x à 10)í
xí
(3x Ź 5)í
xí
16. REASONING Explain why all triangles have at least
two acute angles.
36î
17. CARDS One method of stacking cards is shown.
a. Find the value of x.
b. Describe how to stack the cards with different angles.
Is the value of x limited? If so, what are the limitations?
Explain your reasoning.
Extension 7.3
MSCC3_Red_PE_0703b.indd 289
xî
xî
Angle Measures of Triangles
289
12/11/12 12:16:45 PM