You have the following information:
m∠VUT = 166°
m∠IUT = x + 25
m∠VUI = x + 147
In order to find the measure of m∠IUT, you take into account that:
m∠IUT + m∠VUI = m∠VUT
You replace the algebraic expressions and the constant value of m∠VUT to solve for x the following equation;
(x + 25) + (x + 147) = 166 eliminate parenthesis
x + 25 + x + 147 = 166 simplify similar terms left side
x + x + 25 + 147 = 166
2x + 172 = 166 subtract 72 both sides
2x = 166 - 172
2x = -6 divide by 2 both sides
x = -6/2
x = -3
Next, you repace the previoues value of x into the expression for the measure of the angle ∠IUT:
m∠IUT = x + 25 = -3 + 25 = 22°
Hence, the measure of the angle ∠IUT is m∠IUT = 22°
