72
108 ;)
108 degrees
Yes, the measure of a tangent-chord angle is indeed twice the measure of the intercepted arc. This is a key property of circles in geometry. Specifically, if a tangent and a chord intersect at a point on the circle, the angle formed between them is equal to half the measure of the arc that lies between the points where the chord intersects the circle.
True. The measure of a tangent-tangent angle is indeed half the difference of the measures of the intercepted arcs. This theorem applies to angles formed outside a circle by two tangents that intersect at a point, providing a relationship between the angle and the arcs it intercepts.
The tangent-tangent angle is formed by two tangents drawn from a point outside a circle to points on the circle. To find the measure of the tangent-tangent angle, you take half the difference of the intercepted arcs. In this case, the arcs measure 135 degrees and 225 degrees. Therefore, the measure of the tangent-tangent angle is (\frac{1}{2} (225^\circ - 135^\circ) = \frac{1}{2} (90^\circ) = 45^\circ).
DK
108
True -
false
136
108 ;)
136 degrees
108 degrees
148
It is true that the measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle. When a tangent line intersects a chord of a circle, it creates an angle between the tangent line and the chord, known as the tangent-chord angle. If we draw a segment from the center of the circle to the midpoint of the chord, it will bisect the chord, and the tangent-chord angle will be formed by two smaller angles, one at each end of this segment. Now, the intercepted arc inside the tangent-chord angle is the arc that lies between the endpoints of the chord and is inside the angle. The measure of this arc is half the measure of the central angle that subtends the same arc, which is equal to the measure of the angle formed by the two smaller angles at the ends of the segment that bisects the chord. Therefore, we can conclude that the measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle.
Yes, the measure of a tangent-chord angle is indeed twice the measure of the intercepted arc. This is a key property of circles in geometry. Specifically, if a tangent and a chord intersect at a point on the circle, the angle formed between them is equal to half the measure of the arc that lies between the points where the chord intersects the circle.
True