+394 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
+2440 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.
\(m\angle A=x-16=98-16=82^{\circ}\)
\(m\angle B=2x-155=2*98-155=196-155=41^{\circ}\)
\(m\angle C=\frac{1}{2}x+8=\frac{1}{2}*98+8=49+8=57^{\circ}\)
+2440 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.
\(m\angle A=x-16=98-16=82^{\circ}\)
\(m\angle B=2x-155=2*98-155=196-155=41^{\circ}\)
\(m\angle C=\frac{1}{2}x+8=\frac{1}{2}*98+8=49+8=57^{\circ}\)
