Question

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

Explanation:

Step1: Recall the secant - secant angle formula

The measure of an angle formed by two secants of a circle is given by $\frac{1}{2}(m\overset{\frown}{outer}-m\overset{\frown}{inner})$. Here, $m\overset{\frown}{outer} = 106^{\circ}$ and $m\overset{\frown}{inner}=36^{\circ}$.

Step2: Calculate the measure of $\angle1$

Using the formula $\angle1=\frac{1}{2}(106 - 36)$. First, calculate the difference inside the parentheses: $106-36 = 70$. Then, $\frac{1}{2}\times70=35$.

Answer:

$35^{\circ}$