What is the measure of AU
2 answers:
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.
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The relative speed of the car to the truck while moving towards each other is the sum of the speed of both vehicles.
- The time it takes them to meet is <u>1 hour</u>
Reasons:
The distance between the cities, d = 145 miles
The time it takes a truck to cover the distance = 2.5 hours
The speed of the car = 1.5 × Th speed of the truck
Required:
The time it takes them to meet if they are moving towards each other.
Solution:
Therefore;
The speed of the car, = 1.5 × 58 mph = 87 mph
At the time<em>, t</em>, the truck and the car meet, we have;
Which gives;
87 × t + 58 × t = 145
- The time it takes them to meet, <em>t</em> = <u>1 hour</u>
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