Answer:
Explanation:
Given: The measure of the arc QU=88°, ∠QUA=111°.
To find: The measure of the arc AU.
Construction: Join QX and UX and AX, where X is the center of the circle such that ∠UXA=x.
Solution: It is given that The measure of the arc QU=88°, ∠QUA=111°.
Now, we know that The measure of a minor arc is the same as the measure of the central angle that corresponds to it, therefore
If the minor arc QU=88°, then ∠QXU=88°.
Also, we know that the major central angle is double of the inscribed angle, thus
∠QXA=2(∠QUA)
⇒∠QXA=2(111°)
⇒∠QXA=222°
Using the angle sum property for a point X, we have
∠QXA+∠QXA=360°
⇒222°+88+x=360°
⇒310°+x=360°
⇒x=50°.
Again, The measure of a minor arc is the same as the measure of the central angle that corresponds to it, thus
The measure of the arc AU is same as ∠UXA that is 50°,therefore, the measure of AU is 50°.
Hence, option B is correct.