Question

in the diagram of circle c, what is the measure of ∠1?
17°
35°
70°
71°

Explanation:

Step1: Recall secant angle formula

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:
$$m\angle 1 = \frac{1}{2}(m\text{outer arc} - m\text{inner arc})$$

Step2: Identify intercepted arcs

The outer intercepted arc is $106^\circ$, the inner intercepted arc is $36^\circ$.

Step3: Calculate the angle

Substitute the values into the formula:
$$m\angle 1 = \frac{1}{2}(106^\circ - 36^\circ) = \frac{1}{2}(70^\circ) = 35^\circ$$

Answer:

35°