Question

michael stands outside of a circular opening. he points a flashlight at the opening. the two rays in the diagram represent the range of the light from the flashlight. each ray touches the opening at only one unique point on the circle. what is the measure of the angle formed by the light from the flashlight? show hints 80° 140° 120° 100°

Explanation:

Step1: Recall the circle - angle relationship

The sum of the measures of an arc and its corresponding central - angle is 360°. The measure of the arc intercepted by the two rays of the flashlight is 280°.

Step2: Use the formula for the measure of the angle formed by two tangents

The measure of the angle formed by two tangents to a circle is half the difference of the measures of the intercepted arcs. Let the measure of the angle formed by the flashlight rays be $\theta$, and the measure of the major arc be $m_1 = 280^{\circ}$ and the measure of the minor arc be $m_2=360 - 280=80^{\circ}$. The formula for the angle between two tangents is $\theta=\frac{1}{2}(m_1 - m_2)$.

Step3: Calculate the angle

Substitute $m_1 = 280^{\circ}$ and $m_2 = 80^{\circ}$ into the formula: $\theta=\frac{1}{2}(280 - 80)=\frac{1}{2}\times200 = 100^{\circ}$.

Answer:

D. 100°