Questions and Answers
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?
1/2 (a-b)
What is the measure of angle ABC?
42.5°
What is the value of x? x = ______
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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 ______.
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What is the measure of angle AOC?
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What is the measure of arc AED?
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What is the measure of arc QSR?
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What is the arc measure, x, that the satellite can see at an angle of 20°?
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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°.
Studying That Suits You
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Description
Test your understanding of secants, tangents, and angle measures with this set of flashcards. Each card presents a question or problem related to angle measurements and their properties in geometry. Perfect for reinforcing concepts learned in class.
