Bellwork One-half of the measure of an angle plus its supplement is equal to the measure of the angle. Find the measure of the angle Solve for x 2x 2 -13x-7=0 Clickers
Bellwork Solution One-half of the measure of an angle plus its supplement is equal to the measure of the angle. Find the measure of the angle Solve for x 2x 2 -13x-7=0
Section 10.5
The Concept For the bulk of this chapter we’ve been dealing with the arc of circles Today we’re going to finish out our discussion of arcs and angles
Theorem Theorem If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc A C B D This makes sense if we think about this in terms of an inscribed angle with only one leg
On your own What is the measure of arc ADC 82 o A C B D
On your own What is the measure of arc ABC 82 o A C B D
On your own What is the measure of angle ACB, if arc CD measures 160 o 35 o A C B D
Theorems Theorem If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle A B C D x
Example Find the measure of angle AEC A B C D E 110 o 96 o
On your own What is the measure of angle ABC 225 o A C B D E 255 o
On your own What is the measure of angle ABD 148 o A C B D E 30 o
On your own What is the measure of arc AC 121 o A C B D E 142 o
Theorems Theorem Angles Outside the Circle Theorem If a tangent and a secant, two tangents or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs A B C D
Theorems Find the measure of angle ADB A B D 250 o 110 o C
On your own What is the measure of angle ABD 30 o A C B D E 86 o
On your own What is the measure of angle ADB 65 o A B D 195 o
On your own What is the measure of arc BD 32 o A B D 164 o
On your own What is the measure of arc AB 22 o A B D 120 o
On your own What is the measure of angle of E, if arc ABC is 200 o A B D C E
On your own What is the measure of angle of F? A B D C F 110 o 80 o
On your own What is the measure of angle of F? A B D C F 35 o 110 o 105 o
Homework , 22-25
Most Important Points Angle-Chord Relationships that intercept inside a circle Angle relationship that intersects outside the circle