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1._ Uno de los ángulos complementarios, aumentando en /6 rad es igual al otro. mide cada Angulo?
(90°-a)+30°=a
120°-a=a 2 =120°
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2._ la diferencia de dos ángulos suplementarios es /3 rad. Hallar el complemento Angulo anterior
(180°-a)-(180°-a)=60° 180-a -180-a -2 a=60° a=60°/2
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3._ Dos ángulos son complementarios, y uno de ellos es /10 rad. Mas, que el tripl ¿Cuánto mide cada Angulo?
=18 +3(90 - ) =18 +270 -3 4 = 288 = 288 /4 = 72 °
°
°
°
°
°
°
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4._¿Cuánto mide cada uno de los ángulos suplementarios, si quitando al menor de e agregándose al mayor, este resulta el triple de lo que queda del menor?
(180°- )+20°=3( − 20)
200°-
4 =260°/4
= 65
= 3 °
60 60°
–
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5._ Dos Ángulos son suplementarios ; uno de ellos es disminuido en /12 rad, para agregado al otro, de tal manera de este nuevo Angulo es igual a cuatro veces el resto primero ¿ cuanto mide cada Angulo? Angulo?
)+15 =4(-15 - = 4 -60
(180°-
95
5 =255 /5
=51
°
°
)
°
°
°
°
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6._ Hallar la medida del ángulo que disminuido en un suplementario es igual al trip complementario
-(180 - )=3(90 - ) 2 -180 =270 -3 5 =450 =450 /5 = 90 °
°
°
°
°
°
°
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7._ Uno de los ángulos suplementarios es los 3/5 del otro ángulo ¿Cuánto mide cad
(180°- )=3/5
5(180°- )=3
900°-5 =3
8 =900°
=900 /8 °
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8._ De dos ángulos complementarios, es los 4/3 de uno de ellos mas la sexta parte d forman un ángulo recto ¿ cuanto mide cada ángulo?
)+1/6 =90 120 -4/3 + 1/6 = 90 -7/6 =-30 7 =180 =180 /7 4/3(90°-
°
°
°
°
°
=24,71°
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9._¿Cuanto mide cada ángulo que es igual a su suplemento?
=180 - 2 =180 =180 /2 =90 °
°
°
°
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10._ Los 4/7de un ángulo menos la cuarta parte de su suplemento, dan su suplemen aumentando en /6 rad. ¿ Cuanto mide el ángulo?
4/7-1/4(180°- )=(180 °- )+30°
4/7 -45°+1/4 =210°-
4/7 +1/4 + =255°
51/28
=255°
= 7140°/51
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11._ Dos veces la medida de un ángulo es /6. menos que cuatro veces la medida d complemento ¿Cuál es la medida del ángulo?
2 + 30°=4(90° -
2 =360°-30°-4
6 =330°
=330 /6 °
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12._¿Cual es la diferencia entre el suplemento y el complemento de un ángulo que e los 3/7 de un ángulo recto?
(180°-3/7*90°)-(90°-3/7*90)
180°-90°-3/7*90 °+3/7*90°)
90°
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13._ El doble del complemento de un ángulo mas el triple de un ángulo mas el tripl suplemento es 500°.hallar la medida del ángulo
)+3(180 - )=500 180 -2 + 540 - 3 = 500 -5 =-220 =220 /5 2(90°-
°
°
°
°
=44°
°
°
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14._Los ángulos X,Y,Z son proporcionales a los números 3,5y7 hallar el ángulo X
y
X
Z
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15._ Calcular el valor de dos ángulos suplementarios, de modo que si al quíntuplo d se le disminuye la mitad del mayor, se obtiene el triple del menor aumentando en
)- /2=3(180 - )+10 900 -5 - /2=540 -3 +10 -5 - /2+3 =550 -900 -5/2 =-350 5 =700 5(180°-
°
°
°
°
°
°
=700°/5
°
°
°
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16._ Dos ángulos suplementarios están en la razón 5/4. Hallar sus medidas
/ =5/4 4(180 - )=5 720 -4 =5 9 =720 =720 /9 180°-
°
°
°
°
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17._ Si al suplemento del suplemento de un ángulo se le aumenta el complemento d complemento del mismo ángulo, resulta el cuádruplo del complemento del mismo A Hallar el ángulo
)+90 -(90 - )=4(90 - ) 2 =360 -4 6 =360 =360 /6 =60 180°-(180°-
°
°
°
° °
°
°
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18._ La medida de uno de los ángulos de un par de ángulos complementarios es el d medida del otro mas /20. Encontrar la medida de cada ángulo
=2(90 - )+9 =180 -2+9 3 =189 =189/3 =63 °
°
°
°
°
°
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19._ La diferencia entre los 5/6 del suplemento de un ángulo y el complemento de l del ángulo excede en 5 ° al doble del complemento del ángulo. Calcular la medida d 5/6(180°- )-[90°-
/2]-5 =2(90 - ) 150 -5/6* -90 + /2-5 =180 -2 2 -5/6* + /2=125 5/3* =125 5 =375 °
°
°
°
°
°
°
°
°
=375°/5
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20._ El duplo del suplemento de un ángulo es igual al suplemento de la diferencia entr suplemento y el complemento del ángulo. Calcular la medida del ángulo
)=180 -[(180 - )-(90 - )] 360 -2 =180 -90 2 =270 =270 /2
2(180°-
°
°
°
°
°
°
°
°
=135°
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21._ la suma del complemento de un < ∞ con el suplemento de su ángulo doble, es ig del complemento de un < Si : m < ∞-m < = 3 /20 rad. Calcular el complemento ángulo < ∞
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22._Dos ángulos adyacentes complementarios complementarios están en la razón de 2 a 3. hallar el valo ángulo formado por el bisectriz del ángulo menor con el lado no común
/ (90 - ) = 2/3 3 =2(90 - ) 3 =180 -2 5 =180| °
°
°
=180°/5
=36°
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23._ La suma del suplemento de un ángulo con el complemento de su ángulo doble es 110° al tercio del ángulo. Hallar la medida del ángulo (180°- )+(90°-2)= /3+110° 270°-3- /3=+110° 10/3=160° 10=480° =480°/10
=48°
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24._ Si el suplemento del complemento de un ángulo mas el complemento del supleme ángulo doble es igual al doble del complemento del ángulo .Encontrar la medida del án 180°-(90°- )+90°-(180°-2)=2(90°- ) 3=180°-2 5=180° =180°/5
=36°
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25._ La sexta parte del suplemento del complemento de un ángulo es igual a la mitad d parte del complemento complemento del suplemento suplemento de 50°. Hallar la medida del ángulo
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26._ Los ángulos < BAC agudo y < CAD recto, son s on adyacentes. Determinar la medida ángulo formado por las bisectrices de los ángulos < BAC y < BAD 90°- /2+ /2 90°- + /2 90°/2 45°
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27._ B
D
BD || AE
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28._ En un ángulo llano < A0D se trazan los ángulos adyacentes < A0B,
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BD || CE < C= 150° < B = 13 /18 rad
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30°+<1=180°
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34._ 120
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20 a 30
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45._
< FOB= < AOF < EOF=15 < BOC- < AOB=2 /9 rad Sign up to vote on this title < FOD=? °
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46._ se tiene los rayos OP,OQ,OT . EL ángulo formado por las bisectrices de los án POT y < POQ disminuido en ¾ del complemento de un < X es igual a 4°. Determ X si la diferencia entre los ángulos < POT y < POQ es igual a 20°
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47._ OF bisectriz < COL < COE=?
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48._
< DOC= < DOB < BOE= < EOA < AOF= < FOD < EOL=
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49._ < DOA=< BOC=2< AOB < COD= 3 < BOA < POQ=? < POA=?
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50._ <1=15° < BOC-< AOB=2 /9 rad < FOD=?
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(4) < BOD=
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51._ < MOP=20° < MOQ=80°
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< AOB= < AOF/3 < COD= < FOD/3
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