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1-3 Measuring and Constructing Angles
Warm-Up
M is between N and O.
Find NO.
NM + MO = NO
17 + (3x – 5) = 5x + 2
3x + 12 = 5x + 2
–2
–2
3x + 10 = 5x
–3x
–3x
10 = 2x
2
2
5=x
Holt McDougal Geometry
Seg. Add. Postulate
Substitute the given values
Simplify.
Subtract 2 from both sides.
Simplify.
Subtract 3x from both sides.
Divide both sides by 2.
1-3 Measuring and Constructing Angles
Warm-Up continued
M is between N and O.
Find NO.
NO = 5x + 2
= 5(5) + 2
Substitute 5 for x.
= 27
Simplify.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Quote of the Day
“We are what we repeatedly do.
Excellence, then, is not an act, but a
habit”
- Aristotle
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Check It Out! Example 3b
E is between D and F. Find DF.
DE + EF = DF
(3x – 1) + 13 = 6x
3x + 12 = 6x
– 3x
– 3x
12 = 3x
12 3x
=
3
3
4=x
Holt McDougal Geometry
Seg. Add. Postulate
Substitute the given values
Subtract 3x from both sides.
Simplify.
Divide both sides by 3.
1-3 Measuring and Constructing Angles
Check It Out! Example 3b Continued
E is between D and F. Find DF.
DF = 6x
= 6(4)
Substitute 4 for x.
= 24
Simplify.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
An angle is formed by two rays, with a common
endpoint called the vertex (plural: vertices).
Angles are named by either:
Point on each ray & vertex
Number
Vertex (LEAST PREFERRED)
Angle Name
R, SRT, TRS, or 1
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
The measure of an angle is the absolute value of
the difference of the real numbers that the rays
correspond with on a protractor.
If OC corresponds with c
and OD corresponds with d,
mDOC = |d – c| or |c – d|.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Example 2: Measuring and Classifying Angles
Find the measure of each angle. Then classify
each as acute, right, or obtuse.
A. WXV
mWXV = 30°
WXV is acute.
B. ZXW
mZXW = |130° - 30°| = 100°
ZXW = is obtuse.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Congruent angles are angles that have the same
measure.
In the diagram, mABC = mDEF, therefore:
ABC  DEF.
Arc marks are used to show that the two angles are
congruent.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Example 3: Using the Angle Addition Postulate
mDEG = 115°, and mDEF = 48°. Find mFEG
mDEG = mDEF + mFEG  Add. Post.
115 = 48 + mFEG
Substitute the given values.
–48° –48°
67 = mFEG
Holt McDougal Geometry
Subtract 48 from both sides.
Simplify.
1-3 Measuring and Constructing Angles
An angle bisector is a ray that divides an angle
into two congruent angles.
JK bisects LJM; thus LJK  KJM.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Example 4: Finding the Measure of an Angle
KM bisects JKL, mJKM = (4x + 6)°, and
mMKL = (7x – 12)°. Find mJKM.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Example 4 Continued
Step 1 Find x.
mJKM = mMKL
Def. of  bisector
(4x + 6)° = (7x – 12)°
+12
+12
Substitute the given values.
Add 12 to both sides.
4x + 18
–4x
= 7x
–4x
18 = 3x
6=x
Holt McDougal Geometry
Simplify.
Subtract 4x from both sides.
Divide both sides by 3.
Simplify.
1-3 Measuring and Constructing Angles
Example 4 Continued
Step 2 Find mJKM.
mJKM = 4x + 6
= 4(6) + 6
Substitute 6 for x.
= 30
Simplify.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
mWYZ = (2x – 5)° and mXYW = (3x + 10)°. Find
the value of x.
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Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Check It Out! Example 4a
Find the measure of each angle.
QS bisects PQR, mPQS = (5y – 1)°, and
mPQR = (8y + 12)°. Find mPQS.
Step 1 Find y.
Def. of  bisector
Substitute the given values.
5y – 1 = 4y + 6
y–1=6
y=7
Holt McDougal Geometry
Simplify.
Subtract 4y from both sides.
Add 1 to both sides.
1-3 Measuring and Constructing Angles
Check It Out! Example 4a Continued
Step 2 Find mPQS.
mPQS = 5y – 1
= 5(7) – 1
Substitute 7 for y.
= 34
Simplify.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Check It Out! Example 4b
Find the measure of each angle.
JK bisects LJM, mLJK = (-10x + 3)°, and
mKJM = (–x + 21)°. Find mLJM.
Step 1 Find x.
LJK = KJM
(–10x + 3)° = (–x + 21)°
+x
+x
–9x + 3 = 21
–3
–3
–9x = 18
x = –2
Holt McDougal Geometry
Def. of  bisector
Substitute the given values.
Add x to both sides.
Simplify.
Subtract 3 from both sides.
Divide both sides by –9.
Simplify.
1-3 Measuring and Constructing Angles
Check It Out! Example 4b Continued
Step 2 Find mLJM.
mLJM = mLJK + mKJM
= (–10x + 3)° + (–x + 21)°
= –10(–2) + 3 – (–2) + 21 Substitute –2 for x.
= 20 + 3 + 2 + 21
= 46°
Holt McDougal Geometry
Simplify.
1-3 Measuring and Constructing Angles
Lesson Quiz: Part I
Classify each angle as acute, right, or obtuse.
1. XTS
acute
2. WTU
right
3. K is in the interior of LMN, mLMK =52°,
and mKMN = 12°. Find mLMN.
64°
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Lesson Quiz: Part II
4. BD bisects ABC, mABD =
, and
mDBC = (y + 4)°. Find mABC.
32°
5. Use a protractor to draw an angle with a
measure of 165°.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Lesson Quiz: Part III
6. mWYZ = (2x – 5)° and mXYW = (3x + 10)°.
Find the value of x.
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Holt McDougal Geometry