Answer:
The answer is below
Step-by-step explanation:
In circle O, RT and SU are diameters. Circle O is shown. Line segments S U and R T are diameters. Line segment O V is a radius. Point V is between points R and U. Angle S O R is (13 x) degrees and angle T O U is (15 x minus 8) degrees. If mArc R V = mArc V U , what is mArc V U ? 47° 52° 64° 87°
Given that:
mArc R V = mArc V U, Angle S O R = 13 x degrees and angle T O U = 15 x - 8 degrees
∠SOR = ∠TOU (Vertically opposite angles are equal). Therefore:
13 x = 15x - 8
solving by calculating the value of x to satisfy the equation: Subtracting 13x from both sides
13x - 13x = 15x - 8 - 13x
0 = 15x - 13x - 8
2x - 8 = 0
Adding 8 to both sides:
2x - 8 + 8 = 0 + 8
2x = 8
2x/2 = 8/2
x = 4
∠SOR = 13x = 13(4) = 52°
∠TOU = 15x - 8 = 15(4) - 8 = 60 - 8 = 52°
Let a = mArc R V = mArc V U
Therefore:
mArc R V + mArc V U + ∠TOU = 180 (sum of angles on a straight line)
Substituting:
a + a + 52 = 180
2a = 180-52
2a = 128
a = 128/2
a= 64°
mArc R V = mArc V U = 64°
