In \( \triangle \mathrm{TUV}, \overline{T V} \) is extended through point V to point W , \( \mathrm{m} \angle T U V=(2 x-7)^{\circ}, \mathrm{m} \angle U V W=(10 x-14)^{\circ} \), and \( \mathrm{m} \angle V T U=(3 x+18)^{\circ} \). Find \( \mathrm{m} \angle V T U \). Answer Attempt 1 out of 2 Submit Answer

To solve for \( \mathrm{m} \angle V T U \), we first note that the angles around point V must sum to \( 180^\circ \) because they are on a straight line. Therefore, we can write the equation: \[ \mathrm{m} \angle T U V + \mathrm{m} \angle U V W + \mathrm{m} \angle V T U = 180^\circ \] Substituting the expressions given: \[ (2x - 7) + (10x - 14) + (3x + 18) = 180 \] Now, combine like terms: \[ 2x + 10x + 3x - 7 - 14 + 18 = 180 \] \[ 15x - 3 = 180 \] Now, solve for \( x \): \[ 15x = 180 + 3 \] \[ 15x = 183 \] \[ x = \frac{183}{15} = 12.2 \] Now that we have \( x = 12.2 \), substitute it back into \( \mathrm{m} \angle V T U \): \[ \mathrm{m} \angle V T U = 3x + 18 = 3(12.2) + 18 \] \[ = 36.6 + 18 = 54.6^\circ \] Thus, \( \mathrm{m} \angle V T U = 54.6^\circ \). Let me know if you have any more questions!