Answer :
Step-by-step explanation:
The adjacent angle just to the R of x is 180 - x = 54°
From jamieyorkpress:
Intersecting Chord Theorem. “The measure of an angle formed by two chords that intersect inside a circle is equal to the arithmetic mean of the measures of the two intercepted arcs.”
So 54 ° = (62 + AB)° / 2
AB = 46°
Final answer:
The value of arc AB can be found using the information given and the central angle theorem. If the angle x represents the difference of the measures of arcs AB and CD, then the measure of arc AB is 188 degrees. More information would be needed to solve for arc AB otherwise.
Explanation:
In order to find the value of arc AB, we need more information about the relationship between arcs AB, CD, and the angle x. If we assume that AB and CD are arcs of the same circle and that x is the central angle subtended by arc CD, then x equals the measure of arc CD in degrees according to the central angle theorem.
Given x = 126 degrees, if we let 'a' represent the measure of arc AB, we would need more information, like if x represents the entire circle or if AB and CD are the same length, to solve for 'a'.
On the other hand, if x is the difference between the measures of arc AB and CD, we would solve the equation a - CD = x for 'a'. Substituting the given values, we have a - 62 = 126, which can be rearranged to a = 126 + 62, giving a = 188 degrees.
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