In ΔUVW,
U
W
‾
UW
is extended through point W to point X,
m
∠
U
V
W
=
(
x
+
19
)
∘
m∠UVW=(x+19)
∘
,
m
∠
W
U
V
=
(
x
+
13
)
∘
m∠WUV=(x+13)
∘
, and
m
∠
V
W
X
=
(
5
x
+
14
)
∘
m∠VWX=(5x+14)
∘
. Find
m
∠
W
U
V
.
m∠WUV.
We know that the sum of angles in a triangle is 180 degrees. Therefore,
m∠UVW + m∠WUV + m∠VWX = 180
Substituting the given values, we get:
(x+19) + (x+13) + (5x+14) = 180
Simplifying the equation, we get:
7x + 46 = 180
Subtracting 46 from both sides:
7x = 134
Dividing both sides by 7:
x = 19
Now, we can find m∠WUV:
m∠WUV = x + 13 = 19 + 13 = 32 degrees.
Therefore, m∠WUV is 32 degrees.
To find the measure of angle WUV (m∠WUV), we can use the fact that the sum of angles in a triangle is 180 degrees.
In triangle UVW, we have:
m∠UVW + m∠WUV + m∠VWX = 180
Substituting the given angle measures, we get:
(x+19) + m∠WUV + (5x+14) = 180
Combining like terms and simplifying, we have:
6x + m∠WUV + 33 = 180
Now, let's isolate m∠WUV by subtracting 33 from both sides:
m∠WUV = 180 - 33 - 6x
m∠WUV = 147 - 6x
Therefore, the measure of angle WUV (m∠WUV) is 147 - 6x.