12 multiple-choice questions, progressively harder.
An angle measures 38∘38^\circ38∘. What is the measure of its complement?
Solution
Correct answer: C
Complementary measures total 90∘90^\circ90∘. Subtract the known measure.
90∘−38∘=52∘90^\circ-38^\circ=52^\circ90∘−38∘=52∘
An angle measures 121∘121^\circ121∘. What is the measure of its supplement?
Correct answer: A
Supplementary measures total 180∘180^\circ180∘.
180∘−121∘=59∘180^\circ-121^\circ=59^\circ180∘−121∘=59∘
Which description defines adjacent angles?
Correct answer: D
Adjacency is a position relationship. The angles must share both a vertex and a side, and neither interior may overlap the other.
Two angles form a linear pair. One measures 147∘147^\circ147∘. What is the measure of the other?
Correct answer: B
The noncommon rays of a linear pair are opposite, so the angles fill a straight angle.
180∘−147∘=33∘180^\circ-147^\circ=33^\circ180∘−147∘=33∘
Two distinct lines cross at OOO. The northwest (NW) sector measures 84∘84^\circ84∘. What is the measure of the opposite southeast (SE) sector?
The NW and SE sectors are vertical angles, so they are congruent. The SE sector therefore also measures 84∘84^\circ84∘.
84∘84^\circ84∘
Which pair of measures is complementary?
A complementary pair has total measure 90∘90^\circ90∘.
16∘+74∘=90∘16^\circ+74^\circ=90^\circ16∘+74∘=90∘
The other totals are 180∘180^\circ180∘, 180∘180^\circ180∘, and 32∘32^\circ32∘.
Which pair of measures is supplementary?
The required total is 180∘180^\circ180∘.
45∘+135∘=180∘45^\circ+135^\circ=180^\circ45∘+135∘=180∘
The other totals are 90∘90^\circ90∘, 270∘270^\circ270∘, and 270∘270^\circ270∘.
Angles AAA and BBB are congruent and each measures 47∘47^\circ47∘. Angle CCC complements AAA, and angle DDD complements BBB. What is m∠Dm\angle Dm∠D?
Complements of congruent angles are congruent. Each partner is what remains after subtracting 47∘47^\circ47∘ from 90∘90^\circ90∘.
m∠D=90∘−47∘=43∘m\angle D=90^\circ-47^\circ=43^\circm∠D=90∘−47∘=43∘
Two angles each supplement the same 138∘138^\circ138∘ angle. What is the measure of each supplement?
Each supplement has the same total and the same angle removed, so the two supplements are congruent.
180∘−138∘=42∘180^\circ-138^\circ=42^\circ180∘−138∘=42∘
Three consecutive nonoverlapping sectors fill one complete turn. Two measure 92∘92^\circ92∘ and 123∘123^\circ123∘. Find the third measure.
A complete turn measures 360∘360^\circ360∘, and all three sectors fill it exactly once.
360∘−92∘−123∘=145∘360^\circ-92^\circ-123^\circ=145^\circ360∘−92∘−123∘=145∘
Which statement about every linear pair is true?
A linear pair is adjacent by definition. Its opposite outer rays make the whole opening straight, so its measures total 180∘180^\circ180∘. The two angles need not have equal measures.
Two distinct lines cross. One sector measures 101∘101^\circ101∘. Starting with the next sector and moving once around the crossing, what are the other three measures in order?
Each neighboring pair is a linear pair, so the next sector measures 180∘−101∘=79∘180^\circ-101^\circ=79^\circ180∘−101∘=79∘. The opposite sector equals the first by the vertical-angle theorem. The final sector is opposite the 79∘79^\circ79∘ sector.
Thus the order is 79∘,101∘,79∘79^\circ,101^\circ,79^\circ79∘,101∘,79∘.
180∘−101∘=79∘180^\circ-101^\circ=79^\circ180∘−101∘=79∘
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