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Warm-Up 3.4.16
Determine if each statement is true or false. If it is
false, change one word to make the sentence true.
1. An obtuse triangle has two obtuse angles.
False, “one” instead of “two”
2. A right triangle has two acute angles.
True
3. All sides are the same length in a scalene triangle.
False, “No” instead of “All” or “equilateral” instead of “scalene”
4. An acute triangle has one obtuse angle.
False, “obtuse” instead of “acute”
5. An isosceles triangle has at least two sides that are
the same length.
True
Lesson 1.4
Angle Sum of a Triangle
Find angle measures in a triangle.
Triangle Angle Sum
The sum of the measures of the angles of a triangle is 180°.
Good to Know!
The sum of the angles of a triangle can be shown using the
method below.
A triangle is drawn on a piece of paper and cut out. The
angles are torn apart and lined up. The three angles form a
straight angle. The measure of a straight angle is 180.
Example 1
Find the measure of the missing angle.
The sum of the angles of a triangle is 180°.
Combine like terms.
Subtract 145 from each side of the equation.
Check the solution.
80 + 65 + x = 180
145 + x = 180
–145
–145
x = 35a
 65 + 80 + 35 = 180
= 180
The measure of the missing angle is 35.
Example 2
ΔYOU has the angle measures listed below:
mY = 70
mO = (3x – 10)
mU = 7x
a. Find the value of x.
The angles of a triangle sum to 180. 70 + (3x – 10) + 7x = 180
Combine like terms.
10x + 60 = 180
Subtract 60 from each side of the equation.
– 60 – 60
Divide both sides of the equation by 10.
10x = 120
10
10a
The value of x is 12.
x = 12a
Example 2 Continued…
ΔYOU has the angle measures listed below:
mY = 70
mO = (3x – 10)
mU = 7x
b. Find the measure of each angle.
Write the given expression for each unknown angle.
Substitute 12 for x.
Multiply.
Subtract.
mO = (3x – 10)
= 3(12) – 10
= 36 – 10 a
= 26
a
mO = 26
a
mU = 7x
= 7(12)
= 84 a
mU = 84
 mY + mO + mU = 180
70 + 26 + 84 = 180
180 = 180
The mY = 70, mO = 26 and mU = 84.
Check the solution.
a
Exit Problems
Find the value of x.
1.
2.
x = 47
x = 13