Question

note: assume that all segments ind

1. solve for x.

(3x + 23)°
55°
75°

Explanation:

Step1: Recall inscribed angle theorem

The measure of an inscribed angle is half the sum of the measures of its intercepted arcs.

Step2: Set up the equation

$$3x + 23 = \frac{1}{2}(75 + 55)$$

Step3: Simplify the right-hand side

Calculate the sum inside the parentheses first: $75 + 55 = 130$. Then take half: $\frac{1}{2}(130) = 65$.
$$3x + 23 = 65$$

Step4: Isolate the term with x

Subtract 23 from both sides:
$$3x = 65 - 23$$
$$3x = 42$$

Step5: Solve for x

Divide both sides by 3:
$$x = \frac{42}{3}$$

Answer:

$x = 14$