Final answer:
The measure of angle ∠v is 106 degrees.
Step-by-step explanation:
In triangles vyu and wyx, angle vuy is given as 18 degrees. Angle w is given as 52 degrees. Angle wxy is 24 degrees. To find angle v, apply the angle sum property of triangles, which states that the sum of the interior angles in a triangle is always 180 degrees.
In triangle vyu, the sum of angles vuy, angle v, and angle y is 180 degrees. Given vuy = 18 degrees and wyx = 24 degrees, angle v can be calculated by subtracting the sum of known angles from 180 degrees: angle v = 180° - 18° - 24° = 138°.
However, in triangle wyx, the sum of angles wyx, angle y, and angle w is also 180 degrees. Given wyx = 24 degrees and angle w = 52 degrees, angle y can be found using the same property: angle y = 180° - 24° - 52° = 104°.
As angle y is common to both triangles, the measure of angle v can be found by subtracting angle y from angle v in triangle vyu: angle v = angle v - angle y = 138° - 104° = 34°.
Therefore, the measure of angle v in triangle vyu is 34 degrees.