Question

In ΔVWX, start overline, V, X, end overline
VX
is extended through point X to point Y, m, angle, V, W, X, equals, left parenthesis, 2, x, plus, 4, right parenthesis, degreesm∠VWX=(2x+4)
∘
, m, angle, W, X, Y, equals, left parenthesis, 7, x, minus, 19, right parenthesis, degreesm∠WXY=(7x−19)
∘
, and m, angle, X, V, W, equals, left parenthesis, 2, x, plus, 16, right parenthesis, degreesm∠XVW=(2x+16)
∘
. Find m, angle, V, W, X, .m∠VWX.

Answer 1

To find \( m \angle VWX \) in triangle \( \Delta VWX \), we first need to observe the relationships between the angles given in the problem.

1. We know that \( \angle VWX \) and \( \angle WXY \) are supplementary because line segment \( VX \) is extended to point \( Y \). Therefore, we can say:
\[
m \angle VWX + m \angle WXY = 180^\circ
\]

2. We can substitute the expressions for the angles:
\[
(2x + 4) + (7x - 19) = 180
\]

3. Now, simplify the equation:
\[
2x + 4 + 7x - 19 = 180
\]
\[
9x - 15 = 180
\]

4. Next, add 15 to both sides:
\[
9x = 195
\]

5. Now, divide by 9:
\[
x = 21
\]

6. Now that we have found \( x \), we can substitute it back into the expression for \( m \angle VWX \):
\[
m \angle VWX = 2x + 4 = 2(21) + 4 = 42 + 4 = 46^\circ
\]

Thus, the measure of angle \( VWX \) is:
\[
\boxed{46^\circ}
\]