The exterior angles of triangle UVW are ∠X, ∠Y, and ∠Z, and they are adjacent to ∠U, ∠V, and ∠W, respectively.
If m∠V is 95°, and m∠Z is 121°, what is m∠U?
A. 95°
B. 121
C. 59°
D. 26
The sum of the exterior angles of a triangle is always 360°.
We know that ∠X + ∠U = 360°, so ∠U = 360° - ∠X.
We also know that ∠Y + ∠V = 360°, so ∠V = 360° - ∠Y.
Since we are given that ∠V is 95°, we can substitute this value into the equation to find ∠Y:
95° + ∠Y = 360°
∠Y = 360° - 95°
∠Y = 265°
We are given that ∠Z is 121°, and we can find ∠X using the equation ∠X = 360° - ∠Z:
∠X = 360° - 121°
∠X = 239°
Finally, we can substitute these values into the equation ∠U = 360° - ∠X to find ∠U:
∠U = 360° - 239°
∠U = 121°
Therefore, the measure of ∠U is 121°, so the answer is B. 121.
no 26
Apologies for the mistake. Let's correct the solution.
The exterior angles of a triangle are equal to the sum of the two opposite interior angles. Therefore, ∠X = ∠Y + ∠U, ∠Y = ∠Z + ∠V, and ∠Z = ∠X + ∠W.
We are given that ∠V is 95°. Substituting this value into the equation ∠Y = ∠Z + ∠V, we have:
∠Y = 121° + 95°
∠Y = 216°
Now let's find ∠W by substituting the value of ∠Y into the equation ∠Z = ∠X + ∠W:
121° = ∠X + ∠W. Since ∠X + ∠Y + ∠Z = 360°, we have ∠X + 216° + 121° = 360°.
Simplifying, we get ∠X + 337° = 360°.
Subtracting 337° from both sides gives ∠X = 23°.
Substituting this value of ∠X into the equation ∠W + ∠X = 360°, we get:
∠W + 23° = 360°.
Subtracting 23° from both sides gives ∠W = 337°.
Finally, we can find ∠U by substituting the values of ∠X and ∠Y into the equation ∠X = ∠Y + ∠U:
23° = 216° + ∠U.
Subtracting 216° from both sides gives ∠U = -193°.
However, angles cannot be negative. Therefore, there must be a mistake in the given information or my calculations. Please double-check the values provided.