Inscribed Angles
Ever wondered how angles inside a circle relate to the arcs they create? An inscribed angle is an angle with its vertex on a circle and sides containing chords of the circle. The arc that sits inside this angle is called the intercepted arc.
The most important rule to remember is the Inscribed Angle Theorem: the measure of an inscribed angle equals one-half the measure of its intercepted arc. This means if an arc measures 100°, any inscribed angle that intercepts this arc will measure 50°.
Another helpful theorem states that if two different inscribed angles intercept the same arc, these angles are congruent to each other. This gives us a powerful tool for finding unknown angles in circle problems.
Quick Tip: When solving inscribed angle problems, always look for the relationship between the angle and its intercepted arc first. Remember the 1:2 ratio - the angle is always half the arc measure!
To find missing measures in circle problems, apply these theorems directly. For example, if an inscribed angle measures 45°, its intercepted arc must measure 90°. Similarly, if you know an arc measures 70°, any inscribed angle intercepting it will measure 35°.
