Answer:
The measure of arc DB is 74.57°
Step-by-step explanation:
* Lets explain how to solve the problem
- A secant is a line that intersects a circle in exactly two points.
- A tangent is a line that intersects a circle in exactly one point.
- When a tangent and a secant, intersect outside a circle then the
measure of the angle formed is one-half the positive difference
of the measures of the intercepted arcs.
* Lets solve the problem
∵ CE is a secant intersects circle A at points D, E
∵ CB is a tangent intersects circle A at point B
∵ CE and CB formed angle ECB
∴ m∠ECB = 1/2 (m arc EB - m arc DB)
∵ m arc EB = 96°
∵ m arc DB = 25x + 21
∵ m∠ECB = 5x
∴ 5x = 1/2 [96 - (25x + 21)]
- Multiply both sides by 2
∴ 10x = 96 - 25x - 21 ⇒ simplify
∴ 10x = 75 - 25x
- Add 25x for both sides
∴ 35x = 75 ⇒ divide both sides by 35
∴ x = 75/35 = 15/7
- To find the measure of the arc DB substitute the value of x in its
measure
∵ m arc DB = 25x + 21
∴ m arc DB = 25(15/7) + 21 = 522/7 = 74.57°
* The measure of arc DB is 74.57°
