If the ratio of the degree of&
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If the ratio of the degree of exterior angle of∠A,∠B and∠C that are in the triangle ABC is 5:4:3,then the ratio of the degree of∠A,∠B and∠C is( )
A. 5:4:3
B. 3:4:5
C. 1:2:3
D. 3:2:1
A. 5:4:3
B. 3:4:5
C. 1:2:3
D. 3:2:1
∵外角与内角之和为180°,
∴三角形的三个外角与内角之和为540°,
又三角形的内角和为180°,
∴外角之和为540°-180°=360°,
又∵△ABC∠A、∠B、∠C的外角之比是5:4:3,
∴三个外角分别是150°,120°,90°.
故三角形的三个内角∠A、∠B、∠C分别是30°,60°,90°.
故三个内角的比是∠A:∠B:∠C=30°:60°:90°=1:2:3.
故选C.
∴三角形的三个外角与内角之和为540°,
又三角形的内角和为180°,
∴外角之和为540°-180°=360°,
又∵△ABC∠A、∠B、∠C的外角之比是5:4:3,
∴三个外角分别是150°,120°,90°.
故三角形的三个内角∠A、∠B、∠C分别是30°,60°,90°.
故三个内角的比是∠A:∠B:∠C=30°:60°:90°=1:2:3.
故选C.
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