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You have learned about angles before
(previous course)
• Examine relationships between pairs of
angles.
• Examine relationships of angles formed by
parallel lines and a transversal.
• perpendicular lines
Lines that intersect to form right angles
• vertical angles Two pairs of opposite angles formed by two
intersecting lines. The angles are congruent.
• adjacent angles Two angles that have the same vertex,
•
share a common side, and do not overlap
complementary Two angles whose sum is 90°
angles
• supplementary anglesTwo angles whose sum is 180°
• parallel lines Two lines in a same plane that do not
intersect
• transversal
A line that intersects two parallel lines to
form eight angles
• alternate interior
angles
• alternate exterior
angles
Nonadjacent interior angles found on opposite
sides of the transversal. In parallel lines, these
are congruent.
Nonadjacent exterior angles found on opposite
sides of the transversal. In parallel lines, these
are congruent.
• corresponding angles Angles that have the same position on two
different parallel lines cut by a transversal.
These angles are congruent.
Find a Missing Angle Measure
A. Jun is cutting a tile. Classify the relationship
of a and b.
Answer: The angles are complementary. The sum
of their measures is 90°.
Find a Missing Angle Measure
B. If ma = 53°, what is the measure of b?
mb + 53 = 90
mb + 53 – 53 = 90 – 53
mb = 37
Answer: mb = 37°
Write the equation.
Subtract 53 from each side.
Simplify.
A. Elisa is cutting a piece of fabric. What is the
relationship between a and b?
a
b
A. They are complementary.
B. They are supplementary.
C. They are congruent.
D. They are obtuse.
A.
B.
C.
D.
A
B
C
D
B. If ma = 40°, what is mb?
A. 140°
a
b
B. 220°
C. 50°
D. 90°
A.
B.
C.
D.
A
B
C
D
Find Measures of Angles Formed by Parallel Lines
A. Classify the relationship
between 9 and 13.
Answer: Since 9 and 13 are corresponding angles,
they are congruent.
Find Measures of Angles Formed by Parallel Lines
B. If m13 is 75°, find m11
and m15.
Since 13 and 11 are alternate
interior angles, they are congruent.
So, m11 = 75°.
11 and 15 are corresponding angles
and are congruent. So, m15 = 75°.
Answer: m11 = 75° and m15 = 75°
A. What is the relationship
between 1 and 5?
A. They are corresponding
and congruent.
B. They are adjacent and
supplementary.
C. They are corresponding
and supplementary.
D. They are adjacent and
congruent.
A.
B.
C.
D.
A
B
C
D
B. If m3 = 78°, what is m7?
A. 12°
B. 22°
C. 78°
D. 102°
A.
B.
C.
D.
A
B
C
D
Use Algebra to Find Missing Angle Measures
ALGEBRA Angles DEF and WXY are
complementary angles, with mDEF = 2x and
mWXY = 3x – 20. Find the measures of DEF
and WXY.
Step 1 Find the value of x.
mDEF + mWXY = 90
2x + 3x – 20 = 90
Complementary angles
Replace mDEF with 2x
and mWXY with 3x – 20.
Use Algebra to Find Missing Angle Measures
Combine like terms.
Add 20 to each side.
Simplify.
Divide each side by 5.
Simplify.
Use Algebra to Find Missing Angle Measures
Step 2 Replace x with 22 to find the measure of
each angle.
mDEF = 2x
= 2(22) or 44
mWXY = 3x – 20
= 3(22) – 20 or 46
Answer: mDEF = 44° and mWXY = 46°
Angles RST and ABC are complementary angles
with mRST = 3x and mABC = x + 10. What are
the measures of ABC and RST?
A. mABC = 12° and mRST = 78°
B. mABC = 20° and mRST = 70°
C. mABC = 30° and mRST = 60°
D. mABC = 30° and mRST = 70°
A.
B.
C.
D.
A
B
C
D