Question

exterior angles #1 unique id: 1015
this is the only question in this section.
question
solve for x.
answer attempt 2 out of 3
additional solution no solution
x = submit answer

Explanation:

Step1: Apply the exterior angle theorem for circles

The measure of an angle formed by two secants outside a circle is half the difference of the measures of the intercepted arcs. The formula is \( \angle M=\frac{1}{2}(\text{arc }CK - \text{arc }LN)\). Given \( \angle M = 40^{\circ}\) and \( \text{arc }LN=67^{\circ}\), \( \text{arc }CK = 30x - 3\).
So, \(40=\frac{1}{2}((30x - 3)-67)\)

Step2: Solve the equation

Multiply both sides of the equation by 2: \(40\times2=(30x - 3)-67\)
\(80=30x-70\)
Add 70 to both sides: \(80 + 70=30x\)
\(150=30x\)
Divide both sides by 30: \(x=\frac{150}{30}\)
\(x = 5\)

Answer:

\(x = 5\)