Secants, Tangents, and Angles Assignment

Which formula would be used to find the measure of angle 1?

1/2 (a-b)

A satellite views the Earth at an angle of 20°. What is the arc measure, x, that the satellite can see?

160

Aaron is standing at point C, watching his friends on a Ferris wheel. He knows that he is looking up at a 57° angle and the measure of arc BD is 80°. What is the measure of arc AED?

194

What is the measure of arc QSR?

250

What is the measure of angle ABC?

42.5°

What is the value of x? x =

58

Use the information given in the diagram to prove that m∠JGI = (b - a), where a and b represent the degree measures of arcs FH and JI. Angles JHI and GJH are inscribed angles. We have that m∠JHI = b and m∠GJH = a by the ___________________ Angle JHI is an exterior angle of triangle _____. Because the measure of an exterior angle is equal to the sum of the measures of the remote interior angles, m∠JHI = m∠JGI + m∠GJH. By ___________________ , b = m∠JGI + a. Using the subtraction property, m∠JGI = b - a. Therefore, m∠JGI = (b - a) by the distributive property.

inscribed angle theorem GHJ substitution property

What is the measure of angle AOC? 42° 58° 66° 79°

66

Two tangents each intersect a circle at opposite endpoints of the same diameter. Is it possible for the two tangents to intersect each other outside the circle? Explain why or why not, using the information you learned in this lesson.

No, the tangents cannot intersect outside the circle. When tangents intersect outside a circle, the measure of the angle they form is one half the difference of the intercepted arcs. Since the tangents are at the endpoints of the same diameter, both intercepted arcs would have to measure 180 degrees. This means the angle would have a measure of one half times the difference of 180 and 180, which is 0. An angle with a zero degree measure could not intersect a circle on opposite sides.