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Arcs and Angles Continued

Arcs and Angles Continued. Lesson 9.2B R.4.G.5 Investigate and use the properties of angles ( central and inscribed ) arcs , chords , tangents , and secants to solve problems involving circles. Review. The measure of a central angle is equal to the measure of its intercepted arc

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Arcs and Angles Continued

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  1. Arcs and Angles Continued Lesson 9.2B R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles

  2. Review • The measure of a central angle is equal tothe measure of its intercepted arc • The measure of an inscribed angle is one halfthe measure of its intercepted arc • A tangent line is always perpendicular to a radius drawn to the point of tangency.

  3. What if the angles are neither central nor inscribed? Are the arc measures the same? Are the angle measures the same? What do we do??? 30° x° x° 80°

  4. Angles of Intersecting Secants (Internal) • If two secants intersect in the interior of the circle, the measure of an angle formed is half the sum of the measures of the intercepted arcs of the angle and its vertical angle. In other words… b x° x° a

  5. 44° x° 66° 52° x° 38° Example Now You Try… Find the value of x. Find the value of x.

  6. Angles of Intersecting Secants (External) • If two secants or tangents intersect in the exterior of a circle, the measure of an angle formed is half the difference of the measures of the intercepted arcs. In other words… x° b° a°

  7. Example Now You Try… Find the value of x. Find the value of x. 70° 80° x° x° 80° 60° 180° 180°

  8. Example Now You Try… Find the value of x. Find the value of x. x° x° 95° 50o 120° 105°

  9. Example Now You Try… Find the value of x. Find the value of x. x° x° 80° 215°

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