Download Lesson 10-1

Lesson 11-1 Angle and Line Relationships
Adjacent Angles – two angles that share a common side with the same vertex
Vertical Angles – two angles formed when two lines intersect and the angles are non-adjacent to
each other
Complementary Angles – the sum of the measure of two angles equals 90 degrees
Supplementary Angles – the sum of the measure of two angles equals 90 degrees
Real-World Example 1 Find a Missing Angle Measure
CARPENTRY Mark cuts through the corner of a rectangular
63
board at a 63 angle.
x
a. Classify the relationship between the 63 angle and x.
The angles at the cut point are complementary.
b. What is the measure of x?
Since the angles are complementary, the sum of their measures is
90°.
mx + 63 = 90
mx + 63 – 63 = 90 – 63
mx = 27
Write the equation.
Subtract 63 from each side.
Simplify.
So, mx = 27.
Perpendicular Lines – two lines that form right angles
Parallel Lines – two lines in a plane that never intersect
Transversal – a line that intersects two or more other lines in a plane
Alternate Interior Angles – two angles between parallel lines that are on
opposite sides of the transversal (Note: they must involve using all three lines)
Alternate Exterior Angles – two angles outside the parallel lines that are on
opposite sides of the transversal (Note: they must involve using all three lines)
Corresponding Angles – two angles on the same side of the transversal but one
is interior and the other is exterior (Note: they must involve using all three lines)
Example 2 Find Measures of Angles Formed by Parallel Lines
In the figure at the right, m || n and t is a transversal.
a. Classify the relationship between 6 and 1 and the
relationship between 1 and 5.
6 and 1 are alternate exterior angles.
1 and 5 are corresponding angles.
b. If m6 = 55, find m1 and m5.
Since 6 and 1 are alternate exterior angles, they are congruent. So, m1
= m6 = 55.
Since 1 and 5 are corresponding angles, they are congruent. So, m5
= m1 = 55.
Example 3 Use Algebra to Find Missing Angle Measures
ALGEBRA Angles DEF and GHI are supplementary. If mDEF = x – 6 and mGHI =
2x + 9, find the measure of each angle.
Step 1
Find the value of x.
mDEF + mGHI = 180
(x – 6) + (2x + 9) = 180
3x + 3 = 180
3x = 177
x = 59
Step 2
Supplementary angles
Substitution
Combine like terms.
Subtract 3 from each side.
Divide each side by 3.
Replace x with 59 to find the measure of each angle.
mDEF = x – 6
= 59 – 6 or 53
So, mDEF = 53 and mGHI = 127.
mGHI = 2x + 9
= 2(59) + 9 or 127