Answer:
The value of x = 34° ⇒ first answer
Step-by-step explanation:
* Lets revise some facts about the circle
- A chord of a circle is a straight line segment whose endpoints
both lie on the circle
- When two chords, intersect inside a circle then the measure
of the angles formed is one-half the sum of the measures of the
intercepted arcs.
* Now lets solve the problem
- There are two chords intersect inside the circle
∵ AC and DB are two chords intersect each other at point O
- The measures of the angles between them is 1/2 the measure
of their intercepted arc
∵ ∠AOB subtended by arc AB
∵ ∠COD subtended by arc CD
∴ m∠AOB = m∠COD = 1/2[measure arc AB + measure arc CD]
∵ The measure of arc AB = 45°
∵ The measure of arc CD = 23°
∴ m∠AOB = m∠COD = 1/2[45 + 23] = 1/2[68] = 34°
- The measure of angle AOB represented by x
∴ m∠AOB = x
∴ The value of x = 34°
