Answer:
[tex] \boxed{x = 45°} [/tex]
Step-by-step explanation:
When two chords intersect at a point in a circle, they form arcs, along with angles at the intersection point.
To determine the angle of the arc, we must apply this geometric rule:
[tex] Angle \: formed \: by \: chords = \frac{1}{2}(sum \: of \: intersecting \: arcs) [/tex].
Since we are looking for one of the arcs, we can rearrange this formula to solve for the first arc.
[tex] Angle \: formed \: by \: chords = \frac{1}{2}(sum \: of \: intersecting \: arcs) [/tex] →
[tex] Angle \: formed \: by \: chords = \frac{1}{2}(\overset{\frown}{BA} + \overset{\frown}{CD}) [/tex] →
[tex] 2 × Angle \: formed \: by \: chords = \overset{\frown}{BA} + \overset{\frown}{CD} [/tex] →
[tex] 2 × Angle \: formed \: by \: chords \: – \: \overset{\frown}{CD} = \overset{\frown}{BA} [/tex]
[tex] \overset{\frown}{BA} = 2 × Angle \: formed \: by \: chords \: – \: \overset{\frown}{CD} [/tex]
[Given]
[tex] \overset{\frown}{BA} = x° [/tex]
[tex] \overset{\frown}{CD} = 99° [/tex]
[tex] Angle \: formed \: by \: chords \: = 72° [/tex]
→
[tex] \overset{\frown}{BA} = 2 × Angle \: formed \: by \: chords \: – \: \overset{\frown}{CD} [/tex]
→
[tex] x° = 2 × 72° \: – \: 99° [/tex]
[tex] x° = (2 × 72°) \: – \: 99° [/tex]
[tex] x° = 144° \: – \: 99° [/tex]
[tex] \boxed{x° = 45°} [/tex]
