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ANGLESANGLES
• An angle ( ) is formed by two rays (called sides of the angle) with the same endpoint (called the vertex of the angle).
PARTS OF AN ANGLE Vertex: A
B Sides: AB and AC
exterior of the angle
interior of
the angle
A 1 C
HOW TO NAME AN ANGLE - BAC - CA B - 1 - A
• Angles are measured in degrees.
• The measure of A is written as m A. m A = 45o.
CLASSIFICATION OF ANGLES(according to measure)
xo
ACUTE xo xo
0 < x < 90o RIGHT x = 90o
REFLEX xo 180o < x < 360o xo
OBTUSE STRAIGHT 90o < x < 180o x = 180o
PROTRACTOR POSTULATELet OA and OB be opposite rays in a plane. OA, OB and all the rays with endpoint O that can be drawn on one side of AB can be paired with the real numbers from 0o to 180o in such a way that OA is paired with 0o to and OB is paired with 180o or the way around.
• Angles with the same measure are congruent.
ANGLE ADDITION POSTULATEIf point B is in the interior of AOC, then
mAOB + mBOC = mAOC .
If AOC is a straight angle, then mAOB + mBOC = 180o.
Angle Pairs• Two coplanar angles are adjacent if and only if they satisfy
three conditions:
1. they have a common vertex,
2. they have common side, and
3. they have no common interior points.
AOB and BOC are adjacent. ABC and DEF are not.
• Two angles are complementary if and only if the sum of their measures is equal to 90o. Each angle is the complement of the other.
• Two angles are supplementary if and only if the sum of their measures is equal to 180o . Each angle is the supplement of the other
Find the complement.
What is the complement of 60°?
30°
What is the complement of 35°?
55°
What is the complement of 23°?
67°
What is the complement of 81°?
9°
What is the complement of 77°?
13°
What is the complement of 3°?
87°
What is the complement of 45°?
45°
Find the supplement.
What is the supplement of 30°?
150°
What is the supplement of 112°?
68°
What is the supplement of 95°?
85°
What is the supplement of 47°?
133°
What is the supplement of 8°?
172°
What is the supplement of 164°?
26°
What is the supplement of 146°?
34°
(mixed)
What is the complement of 59°?
31°
What is the supplement of 15°?
165°
What is the complement of 27°?
63°
What is the complement of 100°?
none
What is the supplement of 100°?
80°
What is the complement of the supplement of 146°?
56°
What is the complement of the complement of 10°?
10°
What is the supplement of the supplement of 113°?
113°
What is the complement of the supplement of 110°?
20°
What is the complement of the supplement of 35°?
none°
What is the supplement of the complement of 14°?
114°
What is the supplement of the complement of 88°?
178°
What is the complement of x°?
(90-x)°
What is the supplement of x°?
(180-x)°
If BAC is 20° more than its complement, what is its measure?
55°
An angle measures twice the measure of its complement. What is the angle?
60°
Angle BUM is 30° less than twice its complement. Find its measurement.
50°
An angle and its complement have a ratio of 2:3. What are their measurements?
36°, 54°
The difference between the measures of angle and its complement is 36°. Find their measurements.
63°, 27°
Angle CAT and angle DOG are supplementary. If mCAT is thrice the mDOG, what are their measurements?
135°, 45°
Find the size of the angle whose supplement is equal to six times its complement.
72°
The supplement of an angle measures 40° more than twice its complement. What is the measurement of the angle?
40°
The difference between the measures of two supplementary angles is 500. Find the measure of the larger angle.
115°
Find the measure of R if:a) it is 50° more than its complement.b) it is 12° less than its complement.c) it is thrice its complement.d) it is half its complement.e) it is 58° more than thrice its complement. f) it is twice the measure of its supplement.g) it is 44° less than its supplement.h) its supplement is thrice its complement.i) its complement and supplement add up to 120°.j) its complement is 90° less than its supplement.
