Question

What is the measure of AU

Answer 1

Answer:

Step-by-step 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.

Answer 2

It is 50 degrees just took the test