Podcast
Questions and Answers
What are the measures of angles 1 and 2? m∠1 = ______, m∠2 = ______
What are the measures of angles 1 and 2? m∠1 = ______, m∠2 = ______
50, 130
Which formula would be used to find the measure of angle 1?
Which formula would be used to find the measure of angle 1?
1/2 (a-b)
What is the measure of angle ABC?
What is the measure of angle ABC?
42.5°
What is the value of x? x = ______
What is the value of x? x = ______
Use the information given in the diagram to prove that m∠JGI = (b - a). 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 ______.
Use the information given in the diagram to prove that m∠JGI = (b - a). 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 ______.
What is the measure of angle AOC?
What is the measure of angle AOC?
What is the measure of arc AED?
What is the measure of arc AED?
What is the measure of arc QSR?
What is the measure of arc QSR?
What is the arc measure, x, that the satellite can see at an angle of 20°?
What is the arc measure, x, that the satellite can see at an angle of 20°?
Is it possible for two tangents to intersect each other outside the circle?
Is it possible for two tangents to intersect each other outside the circle?
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Study Notes
Angles and Measurements
- Angle measures: m∠1 = 50°, m∠2 = 130°.
- Angle ABC measures 42.5°.
- The measure of arc AED calculated based on the given information is 194°.
- Angle AOC measures 66°.
- The measure of arc QSR is 250°.
Formulas and Theorems
- To find the measure of an angle formed by two secants, use the formula: 1/2 (a - b) where a and b are the measures of the intercepted arcs.
- Inscribed angles: m∠JHI = b, m∠GJH = a based on the inscribed angle theorem.
- Proving angle relationships involves substitutive properties leading to m∠JGI = b - a.
Tangents and Circle Properties
- When two tangents intersect outside a circle, the angle formed is half the difference of the intercepted arcs.
- If tangents intersect at endpoints of the same diameter, they cannot intersect outside the circle; the resulting angle would be 0° since both intercepted arcs measure 180°.
Additional Values
- Value of x in a given context is determined to be 58.
- The satellite viewing the Earth at an angle of 20° has an arc measure, x, of 160°.
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