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mr Goodwill [35]
3 years ago
12

What is measure of Arc AC if the m ∠BAC = 28°?

Mathematics
2 answers:
liq [111]3 years ago
8 0
14 degrees.  It equals half the intercepted arc.
(See attached graphic)


mart [117]3 years ago
5 0

Answer:

C. 56^{\circ}

Step-by-step explanation:

We have been given an image of a circle. We are asked to find the measure of arc AC.

We will use tangent-secant theorem, which states that the angle formed by a tangent to a circle and a chord is equal to half the angle measure of the intercepted arc.

Using above theorem we can set an equation to find measure of arc AC as:

m\angle BAC=\frac{1}{2}\times \text{ Measure of arc AC}

28^{\circ}=\frac{1}{2}\times \text{ Measure of arc AC}

Multiplying both sides of our equation by 2, we will get,

2*28^{\circ}=\frac{1}{2}*2\times \text{ Measure of arc AC}

56^{\circ}=\text{ Measure of arc AC}

Therefore, the measure of arc AC is 56 degrees and option C is the correct choice.

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1. In which quadrant or on which axis do each of the points (-2,4) , (3,-1) ,(-1,0), (1,2) and (-3,-5) lie? Verify your answer b
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Point (-2 , 4) lies in the 2nd quadrant

Point (3 , -1) lies in the 4th quadrant

Point (-1 , 0) lies on the negative part of the x-axis

Point (1 , 2) lies in the 1st quadrant

Point (-3 , -5) lies in the 3rd quadrant

Step-by-step explanation:

Let us revise the signs of the coordinates in each quadrant

  • x and y coordinates are positive in the 1st quadrant
  • x-coordinate is negative and y-coordinate is positive in the 2nd quadrant
  • x and y coordinates are negative in the 3rd quadrant
  • x-coordinate is positive and y-coordinate is negative in the 4th quadrant
  • The general point on the positive part of x-axis is (x , 0), and on the negative part of x-axis is (-x , 0)
  • The general point on the positive part of y-axis is (0 , y), and on the negative part of y-axis is (0 , -y)

Now let us check the points

Point (-2 , 4) ⇒ red point

∵ x = -2 and y = 4

∵ x-coordinate is negative and y-coordinate is positive

∴ Point (-2 , 4) lies in the 2nd quadrant

Point (3 , -1) ⇒ blue point

∵ x = 3 and y = -1

∵ x-coordinate is positive and y-coordinate is negative

∴ Point (3 , -1) lies in the 4th quadrant

Point (-1 , 0) ⇒ green point

∵ x = -1 and y = 0

∵ x-coordinate is negative and y-coordinate is zero

∴ Point (-1 , 0) lies on the negative part of the x-axis

Point (1 , 2) ⇒ purple point

∵ x = 1 and y =2

∵ x and y coordinates are positive

∴ Point (1 , 2) lies in the 1st quadrant

Point (-3 , -5) ⇒ black point

∵ x = -3 and y = -5

∵ x and y coordinates are negative

∴ Point (-3 , -5) lies in the 3rd quadrant

<em>Look to the attached graph for more understand</em>

Learn more:

You can learn more about the four quadrant in brainly.com/question/9381523

#LearnwithBrainly

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