In triangle ABC, the measure of angle B is three times that of angle A. The measure of angle C is 20 degrees more than that of angle A. How do you find the angle measures?

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In triangle ABC, the measure of angle B is three times that of angle A. The measure of angle C is 20 degrees more than that of angle A. How do you find the angle measures?

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Answer 1 · 2016-10-28T01:59:55

$∠ A = 32^{\circ}$ $angleA=32^@$
$∠ B = 96^{\circ}$ $angle B=96^@$
$∠ C = 52^{\circ}$ $angleC=52^@$

Explanation:

In a triangle, the three interior angles always add up to 180°:

Let $∠ A = x$ $angleA=x$
$\Rightarrow ∠ B = 3 x$ $=> angleB=3x$
$\Rightarrow ∠ C = x + 20$ $=> angleC=x+20$

$∠ A + ∠ B + ∠ C = 180^{\circ}$ $angleA + angleB + angleC = 180^@$
$\Rightarrow x + 3 x + x + 20 = 180$ $=> x+3x+x+20=180$
$\Rightarrow 5 x + 20 = 180$ $=> 5x+20=180$
$\Rightarrow 5 x = 160$ $=> 5x=160$
$x = 32$ $x=32$

Therefore, $∠ A = x = 32^{\circ}$ $angleA=x=32^@$
$∠ B = 3 x = 3 \cdot 32 = 96^{\circ}$ $angle B=3x=3*32=96^@$
$∠ C = x + 20 = 32 + 20 = 52^{\circ}$ $angleC=x+20=32+20=52^@$

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In triangle ABC, the measure of angle B is three times that of angle A. The measure of angle C is 20 degrees more than that of angle A. How do you find the angle measures?

1 Answer

Explanation:

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