in triangle ABC, angleC = 3angleB = 2(angleA+angleB). Find all three angles.
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Answer:
Given that ∠C=3∠B=2(∠A+∠B)
Solving above equality we get
∠B=2∠A, ∠C=6∠A
But, in a triangle ΔABC we know that ∠A+∠B+∠C=180∘
∴∠A+2∠A+6∠A=180∘
9∠A=180∘
∠A=180∘9
∠A=20∘
∴∠B=2∠A=2(20∘)=40∘
∴∠C=6∠A=6(20∘)=120∘
Step-by-step explanation:
I think it's correct
Answered by
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Step-by-step explanation:
- we know that some of three angles of triangle equal to 180 degree
- therefore angle A + angle B+ angle C equal to 180 degree
- in given angle C= 2(angle A + angle B)
- angle A + angle B = (angle C)/2
- angle A + angle B + angle C= (angle C)/2 + angle C
- 180degree= 3/2(angleC)
- angleC={2/3}×180
angleC=120degree
- angle A + angle B = 180 degree -120 degree= 60 degree
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