Answer:
The measure of angle ABC is 36° ⇒ 1st answer
Step-by-step explanation:
Let us revise some important facts in the circle
- The measure of the center angle is equal to the measure of its subtended arc
- The measure of the inscribed angle is equal to half the measure of the central angle subtended by the same arc
- The vertex of a central angle is the center of the circle and its sides are radii in the circle
- The vertex of an inscribed angle is a point on the circle, and its sides are chords in the circle
In circle D
∵ D is the center of the circle
∵ A and C lie on the circle
- DA and DC are radii
∴ ∠ADC is a central angle subtended by arc AC
∴ m∠ADC = m of arc AC
∵ m∠ADC = (7x + 2)°
∵ m of arc AC = (8x - 8)°
- Equate them to find x
∴ 8x - 8 = 7x + 2
- subtract 7x from both sides
∴ x - 8 = 2
- Add 8 to both sides
∴ x = 10
Substitute the value of x in the measure of ∠ADC
∵ m∠ADC = 7(10) + 2 = 70 + 2
∴ m∠ADC = 72°
∵ AB and BC are two chords in circle D
∴ ∠ABC is an inscribed angle subtended by arc AC
∵ ∠ADC is a central angle subtended by arc AC
- By using the 2nd fact above
∴ m∠ABC = m∠ADC
∴ m∠ABC = × 72
∴ m∠ABC = 36°
Answer:
O
Step-by-step explanation: Just divide each kilometer by hrs for each one (sry if this doesn't make sense) O: 60 divided by 5= 12 M: 80 divided by 5=16 N: 110 divided by 5= 22. Therefore O= 12 kilometers per hour, which means its the slowest ( I did this question in khan and got it right)
Answer:
Step-by-step explanation:
11 is the amount per hour, x stands for the number of hours, and he needs to earn at least 90 dollars.
Answer:
Step-by-step explanation:
5.7
Answer:
-4 mph/sec
Step-by-step explanation: