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1 [2026 陕西咸阳期中]将$2.36°$用度、分、秒表示正确的是（
A.$2°36'$
B.$2°21'36''$
C.$2°30'6''$
D.$2°18'36''$
B
）A.$2°36'$
B.$2°21'36''$
C.$2°30'6''$
D.$2°18'36''$
答案
1.B 【解析】0.36×60' = 21. 6',0. 6×60'' = 36'',故将2. 36°用度、分、秒表示为2°21'36'',故选B.
2 下列角度换算错误的是 （
A.$10.6° = 10°36''$
B.$900'' = 0.25°$
C.$1.5° = 90'$
D.$54°16'12'' = 54.27°$
A
）A.$10.6° = 10°36''$
B.$900'' = 0.25°$
C.$1.5° = 90'$
D.$54°16'12'' = 54.27°$
答案
2.A 【解析】A 选项,10.6°=10°36',原式错误,符合题意;B 选项,900''= 0. 25°,原式正确,不符合题意;C 选项,1. 5°= 60'+( 0. 5×60 )' = 90',原式正确,不符合题意;D 选项,54°16'12''= 54. 27°,原式正确,不符合题意. 故选 A.
3 已知$∠α=30°18'$，$∠β=30.18°$，$∠\gamma=30.3°$，则相等的两个角是（
A.$∠α=∠β$
B.$∠α=∠\gamma$
C.$∠β=∠\gamma$
D.无法确定
B
）A.$∠α=∠β$
B.$∠α=∠\gamma$
C.$∠β=∠\gamma$
D.无法确定
答案
3.B 【解析】因为 $∠α = 30°18' = 30. 3°, ∠β = 30. 18°, ∠γ= 30. 3°,$所以 $∠α=∠γ$. 故选 B.
4(1)将$57.32°$用度、分、秒表示；
(2)将$10°6'36''$用度表示.
(2)将$10°6'36''$用度表示.
答案
4.【解】(1)因为 $1°=60'$,所以 $0. 32°= 19. 2'$. 因为 $1' = 60''$, 所以 $0. 2' = 12''$, 所以 $57. 32° = 57°19'12''$.
(2)因为 $1'=60''$,所以 $36''=0. 6'$. 因为 $1°=60'$,所以 $6. 6'=0. 11°$,所以 $10°6'36''= 10. 11°$.
(2)因为 $1'=60''$,所以 $36''=0. 6'$. 因为 $1°=60'$,所以 $6. 6'=0. 11°$,所以 $10°6'36''= 10. 11°$.
5 若∠1+∠2=90°,∠1=58°25',那么∠2的度数是（
A.31°75'
B.31°35'
C.41°75'
D.41°25'
B
）A.31°75'
B.31°35'
C.41°75'
D.41°25'
答案
5.B 【解析】根据题意, $∠2 = 90°-∠1 = 89°60'-58°25' = 31°35'$. 故选 B.
6[2026山东菏泽期末]计算:$72°35'÷2+18°33'×4=$
110°29'30''
.答案
6. 110°29'30'' 【解析】因为 $72°35'÷2 = 72°÷2 + 35'÷2 = 36°+17. 5' = 36°+17'+30'' = 36°17'30''$, $18°33'×4 = 72°132' = 74°12'$, 所以 $72°35'÷2 + 18°33'×4 = 36°17'30''+74°12' = 110°29'30''$.
7 计算:
(1)$48°39'+67°31'$.
(2)$47°53'43''+53°47'42''$.
(3)$92°56'3''-46°57'54''$.
(4)$23°53'×2-17°43'$.
(5)$15°24'+32°47'-6°55'$.
(6)$102°43'21''÷3$.
(1)$48°39'+67°31'$.
(2)$47°53'43''+53°47'42''$.
(3)$92°56'3''-46°57'54''$.
(4)$23°53'×2-17°43'$.
(5)$15°24'+32°47'-6°55'$.
(6)$102°43'21''÷3$.
答案
7.【解】(1)$48°39'+67°31' = 115°70' = 116°10'$.
(2) $47° 53' 43'' + 53° 47' 42'' = 100° 100' 85'' = 101°41'25''$.
(3)$92°56'3''-46°57'54'' = 91°+115'+63''-46°-57'-54'' = 45°+58'+9'' = 45°58'9''$.
(4) $23°53'×2 - 17°43' = 46°106' - 17°43' = 29°63' = 30°3'$.
(5) $15°24'+32°47'-6°55' = 47°71' - 6°55' = 41°16'$.
(6) $102°43'21''÷3 = 102°42'81''÷3 = 34°14'27''$.
(2) $47° 53' 43'' + 53° 47' 42'' = 100° 100' 85'' = 101°41'25''$.
(3)$92°56'3''-46°57'54'' = 91°+115'+63''-46°-57'-54'' = 45°+58'+9'' = 45°58'9''$.
(4) $23°53'×2 - 17°43' = 46°106' - 17°43' = 29°63' = 30°3'$.
(5) $15°24'+32°47'-6°55' = 47°71' - 6°55' = 41°16'$.
(6) $102°43'21''÷3 = 102°42'81''÷3 = 34°14'27''$.
