Download WORKSHEET #6 I will be able to solve problems using the Angle

Name _______________________
WORKSHEET #6
Upward Bound Summer 2011: Geometry
OBJECTIVE:
I will be able to solve problems using the Angle Addition Postulate and angle bisectors.
I will be able to identify and solve problems using angle relationships including vertical angles,
complementary angles and supplementary angles.
NEW CONCEPT:
New Vocabulary → Angle Addition Postulate, angle bisector, vertical angles, complementary angles,
supplementary angles.
The Angle Addition Postulate:
“If
= n, then
= n”
+
A
X
B
C
If
= 45°,
then
= 28°,
= ________________
• Supplementary angles add up to 180°
________ and ________ are supplementary angles
• Complementary angles add up to 90°
________ and ________ are complementary angles
• Vertical angles are congruent
________ and ________ are vertical angles
• An Angle Bisector is a __________________________divides an angle into two congruent angles.
___________ and ___________ are congruent
In the diagram,
⃗⃗⃗⃗⃗ bisects
A
X
B
C
Example 1: In the diagram below,
o
= 25°
o
= (4x + 12)°
o
= 102°
Solve for x and find
NOTES AND EXAMPLES:
. Also,
Example 2: Solve for x and find
Example 3: Find the measures of two supplementary angles if the measure of the larger angle is 31 ⁰
bigger than the smaller angle.
Example 4: Find the measures of two complementary angles if the difference in size between the
two angles is 21⁰.
Example 5: Find the measures of two supplementary angles if one angle is one-fourth the measure
of the other.
Example 6: The measure of an angle is 10 more than 3 times the size of its complement. Find the
measures of both angles.
Example 7: The measure of an angle is 62 less than 10 times the size of its supplement. Find the
measures of both angles.
Example 8:
and find
Example 9:
and find
and
are supplements.
= x + 35 and
= 4x – 5. Solve for x
and
are complements.
= 3x + 5 and
= 11x + 1. Solve for x
.
.