The measure of an angle can only be a whole number of degrees, we round up to the nearest whole number, resulting in mY = 70 degrees.
Based on the image provided, the measure of angle Y in the triangle is 42 degrees. This can be determined using the angle sum property of a triangle, which states that the sum of the interior angles of a triangle is always equal to 180 degrees.
In this case, we are given that the measure of angle X is (6x - 23) degrees and the measure of angle Z is (4x + 9) degrees. Let mY represent the measure of angle Y.
Applying the angle sum property, we can write the following equation:
mY + (6x - 23) degrees + (4x + 9) degrees = 180 degrees
Combining like terms, we get:
10x + 4 degrees = 180 degrees
Subtracting 4 from both sides, we have:
10x = 176 degrees
Dividing both sides by 10, we find x = 17.6 degrees
Therefore, the measure of angle Y is:
mY = (4 * 17.6 degrees) + 9 degrees = 69.2 degrees
Since the measure of an angle can only be a whole number of degrees, we round up to the nearest whole number, resulting in mY = 70 degrees.