12 multiple-choice questions, progressively harder.
What is the complement of a 30∘30^\circ30∘ angle?
Solution
Correct answer: A
Complementary angles sum to 90∘90^\circ90∘, so subtract from 90∘90^\circ90∘.
90∘−30∘=60∘90^\circ - 30^\circ = 60^\circ90∘−30∘=60∘
What is the supplement of a 110∘110^\circ110∘ angle?
Correct answer: C
Supplementary angles sum to 180∘180^\circ180∘, so subtract from 180∘180^\circ180∘.
180∘−110∘=70∘180^\circ - 110^\circ = 70^\circ180∘−110∘=70∘
In the figure, a ray meets a straight line, forming a linear pair. One angle measures 65∘65^\circ65∘. What is the measure of the other angle, marked xxx?
A linear pair sums to 180∘180^\circ180∘, so subtract from 180∘180^\circ180∘.
x=180∘−65∘=115∘x = 180^\circ - 65^\circ = 115^\circx=180∘−65∘=115∘
In the figure, three angles meet at a point and fill the full turn around it. Two of them measure 120∘120^\circ120∘ and 90∘90^\circ90∘. What is the third angle, marked xxx?
Correct answer: B
Angles around a point sum to 360∘360^\circ360∘.
x=360∘−(120∘+90∘)=360∘−210∘=150∘x = 360^\circ - (120^\circ + 90^\circ) = 360^\circ - 210^\circ = 150^\circx=360∘−(120∘+90∘)=360∘−210∘=150∘
What is the supplement of a 45∘45^\circ45∘ angle?
Correct answer: D
180∘−45∘=135∘180^\circ - 45^\circ = 135^\circ180∘−45∘=135∘
In the figure, two straight lines cross and one angle measures 70∘70^\circ70∘. What is the measure of the adjacent angle next to it (which forms a straight line with it), marked xxx?
An adjacent angle forms a straight line with the 70∘70^\circ70∘ angle, so they sum to 180∘180^\circ180∘.
x=180∘−70∘=110∘x = 180^\circ - 70^\circ = 110^\circx=180∘−70∘=110∘
What is the supplement of a 90∘90^\circ90∘ angle?
180∘−90∘=90∘180^\circ - 90^\circ = 90^\circ180∘−90∘=90∘
A right angle is its own supplement.
In the figure, a ray meets a straight line, forming a linear pair. One angle measures 138∘138^\circ138∘. What is the measure of the other angle, marked xxx?
x=180∘−138∘=42∘x = 180^\circ - 138^\circ = 42^\circx=180∘−138∘=42∘
An angle is twice the size of its complement. What is the measure of the angle?
Let the angle be xxx, so its complement is 90∘−x90^\circ - x90∘−x. The angle is twice its complement.
x=2(90∘−x) ⟹ 3x=180∘ ⟹ x=60∘x = 2(90^\circ - x) \implies 3x = 180^\circ \implies x = 60^\circx=2(90∘−x)⟹3x=180∘⟹x=60∘
Check: its complement is 30∘30^\circ30∘, and 60∘60^\circ60∘ is twice 30∘30^\circ30∘.
The complement of an angle measures 25∘25^\circ25∘. What is the original angle?
90∘−25∘=65∘90^\circ - 25^\circ = 65^\circ90∘−25∘=65∘
Two angles whose measures add up to 90∘90^\circ90∘ are called what?
Two angles are complementary when their measures sum to 90∘90^\circ90∘.
Angles summing to 180∘180^\circ180∘ are supplementary instead.
Two angles whose measures add up to 180∘180^\circ180∘ are called what?
Two angles are supplementary when their measures sum to 180∘180^\circ180∘.
Angles summing to 90∘90^\circ90∘ are complementary instead.
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