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# Find the measure of each angle in triangle ABC.

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Find the measure of each angle in triangle ABC. Triangle A B C has angles labeled as follows: A, (x minus 16) degrees; B, (2x minus 155) degrees; C, (one half x plus 8) degrees. left parenthesis 2 x minus 155 right parenthesis degrees(2x−155)° left parenthesis one half x plus 8 right parenthesis degrees12x+8° left parenthesis x minus 16 right parenthesis degrees(x−16)° ABC

The measure of angle A is

The measure of angle B is

The Measure of angle C is

#1
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The triangle sum theorem states that the sum of the measures of the interior angles of a triangle equals 180 degrees. Using this theorem alone, one can find the measure of all the angles.

 $$m\angle A+m\angle B+m\angle C=180$$ Plug in the measure for all these angles by using substitution. $$x-16+2x-155+\frac{1}{2}x+8=180$$ Combine like terms. $$3x+\frac{1}{2}x-163=180$$ Add 163 to both sides. $$\frac{6}{2}x+\frac{1}{2}x=343$$ Meanwhile, I converted 3x to a fraction that I can combine with the other lingering fraction. $$\frac{7}{2}x=343$$ Multiply by 2 on both sides. $$7x=686$$ Divide by 7 on both sides. $$x=98$$

Now, plug in this value for the angle measure expressions.

$$m\angle A=x-16=98-16=82^{\circ}$$

$$m\angle B=2x-155=2*98-155=196-155=41^{\circ}$$

$$m\angle C=\frac{1}{2}x+8=\frac{1}{2}*98+8=49+8=57^{\circ}$$

TheXSquaredFactor  Dec 1, 2017
Sort:

#1
+1711
+2

The triangle sum theorem states that the sum of the measures of the interior angles of a triangle equals 180 degrees. Using this theorem alone, one can find the measure of all the angles.

 $$m\angle A+m\angle B+m\angle C=180$$ Plug in the measure for all these angles by using substitution. $$x-16+2x-155+\frac{1}{2}x+8=180$$ Combine like terms. $$3x+\frac{1}{2}x-163=180$$ Add 163 to both sides. $$\frac{6}{2}x+\frac{1}{2}x=343$$ Meanwhile, I converted 3x to a fraction that I can combine with the other lingering fraction. $$\frac{7}{2}x=343$$ Multiply by 2 on both sides. $$7x=686$$ Divide by 7 on both sides. $$x=98$$

Now, plug in this value for the angle measure expressions.

$$m\angle A=x-16=98-16=82^{\circ}$$

$$m\angle B=2x-155=2*98-155=196-155=41^{\circ}$$

$$m\angle C=\frac{1}{2}x+8=\frac{1}{2}*98+8=49+8=57^{\circ}$$

TheXSquaredFactor  Dec 1, 2017

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