Question

12. In AABC, if 3 ZA = 62B = 82C, calculate the measures of ZA, ZB and ZC.​

Answer 1

Answer:

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Given:

In ∆ABC , 3∠A= 4∠B= 6∠C

Let x= 3∠A= 4∠B= 6∠C

X=3∠A

∠A= x/3

X=4∠B

∠B= x/4

X=6∠C

∠C= x/6

By angle sum property

∠A+∠B+∠C= 180°

Put the value of ∠A, ∠B, ∠C

X/3+x/4+x/6= 180°

L.c.m of 3,4,6 = 12

(4x + 3x +2x) /12 = 180°

9x = 12 × 180

X= (12× 180) /9

X= 240°

∠A= x/3

∠A= 240/3 = 80°

∠B= x/4

∠B= 240/4= 60°

∠C= x/6

∠C= 240/6 = 40°

_____________________________

Hence the angles be

∠A=80°

∠B=60°

∠C= 40°

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Step-by-step explanation: