Question

In a tiangle ABC, the measure of angle B is two-third of the measure of angle A.The measure of angle C is 20 degree more than the measure of angle A.find the measure of three angles​

Answer 1

Answer:

\angle A=60^{\circ}∠A=60

∘

, \angle B=40^{\circ}∠B=40

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, and \angle C=80^{\circ}∠C=80

∘

Explanation:

Given: In triangle ABC the measure of angle B is two - third of the measure of angle A. The measure of angle C is 20 degree more than the measure of angle A

To find: Measure of the three angles

Solution:

Let the measure of angle A be x^{\circ}x

∘

. So, measure of angle B is \frac{2}{3}x^{\circ}

3

2

x

∘

, and measure of angle C is (x+20)^{\circ}(x+20)

∘

Now, we know that

\angle A+\angle B+\angle C=180^{\circ}∠A+∠B+∠C=180

∘

[Angle sum property]

x+\frac{2}{3}x+x+20=180^{\circ}x+

3

2

x+x+20=180

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2x+\frac{2}{3}x+20=180^{\circ}2x+

3

2

x+20=180

∘

2x+\frac{2}{3}x=160^{\circ}2x+

3

2

x=160

∘

8x=480^{\circ}8x=480

∘

x=60^{\circ}x=60

∘

So, \angle A=60^{\circ}∠A=60

∘

, \angle B=\frac{2}{3}\times60^{\circ}=40^{\circ}∠B=

3

2

×60

∘

=40

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, and \angle C=(60+20)^{\circ}=80^{\circ}∠C=(60+20)

∘

=80

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Wish this hepled you..