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 intersecting outside a circle is given by $\frac{1}{2}(m\overset{\frown}{major}-m\overset{\frown}{minor})$. Let the major arc be $105^{\circ}$ and the minor arc be $35^{\circ}$. The angle $\angle 1$ is formed by two secants outside the circle.

Step2: Apply the formula

We know that $m\angle1=\frac{1}{2}(m\overset{\frown}{major}-m\overset{\frown}{minor})$. Substitute $m\overset{\frown}{major} = 105^{\circ}$ and $m\overset{\frown}{minor}=35^{\circ}$ into the formula: $m\angle1=\frac{1}{2}(105 - 35)$.

Step3: Calculate the value

First, calculate the value inside the parentheses: $105-35 = 70$. Then, $\frac{1}{2}\times70=35^{\circ}$.

Answer:

$35^{\circ}$