Final answer:
The measure of arc LB is 52.7°, which is found by setting up and solving an algebraic equation based on the given angle measure and the property that the angle is half the sum of the arc measures.
Step-by-step explanation:
To solve the equation for the measure of arc LB given that the measure of angle is 45.6° and is equal to one-half the sum of the measure of arc LB and the measure of arc 38.5°, we can set up an algebraic equation and solve for the measure of arc LB.
Let's denote the measure of arc LB as x. The equation we will solve is:
45.6° = 0.5 × (x + 38.5°)
Multiply both sides by 2 to get rid of the fraction:
91.2° = x + 38.5°
Now, subtract 38.5° from both sides to isolate x:
x = 91.2° - 38.5°
x = 52.7°
Therefore, the measure of arc LB is 52.7°.