Question

1. solve for x. (7x - 1)° 65° 161°

Explanation:

Step1: Recall exterior secant angle rule

The measure of an angle formed by two secants intersecting outside a circle is half the difference of the measures of the intercepted arcs. The formula is:
$$(7x - 1)^\circ = \frac{1}{2} \times (161^\circ - 65^\circ)$$

Step2: Calculate arc difference

Compute the difference of the intercepted arcs:
$$161 - 65 = 96$$

Step3: Simplify right-hand side

Find half of the arc difference:
$$\frac{1}{2} \times 96 = 48$$

Step4: Solve for x

Set up and solve the linear equation:
$$7x - 1 = 48$$
$$7x = 48 + 1$$
$$7x = 49$$
$$x = \frac{49}{7} = 7$$

Answer:

$x=7$