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katrin [286]
3 years ago
12

What is m CD ? Plzz help

Mathematics
1 answer:
pickupchik [31]3 years ago
8 0

Given:

Arc(AB) = 78 degrees

Measure of angle CMD = 106 degrees

To find:

The measure of arc CD.

Solution:

Secant intersection theorem: If two secant of a circle intersect each other inside the circle, then the intersection angle is the average of intercepted arcs.

Using secant intersection theorem, we get

m\angle CMD=\dfrac{1}{2}(Arc(AB)+Arc(CD))

106^\circ=\dfrac{1}{2}(78^\circ+Arc(CD))

Multiply both sides by 2.

212^\circ=78^\circ+Arc(CD)

212^\circ-78^\circ=Arc(CD)

134^\circ=Arc(CD)

Therefore, the measure of arc CD is 134 degrees and the correct option is C.

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4 0
3 years ago
Jess is 12 years less than half as old as Mac. The sum of their age is 87. How old is each person?
laila [671]

Answer:

The age of each person is:

  • Jess is <u>21</u> years old.
  • Mac is <u>66</u> years old.

Step-by-step explanation:

To solve this problem you must make two equations. First, we name Jess and Mac as variables:

j = Jess age.

m = Mac age.

Now we make the equations, the first equation has the information "Jess is 12 years less than half as old as Mac":

1. j=(\frac{m}{2})-12

The second equation has the information "The sum of their age is 87":

2. j+m=87

Now, we replace the first equation in the second one:

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And we operate:

  • \frac{m-24}{2} +m=87
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We clear the variable m:

  • 3m-24=87*2
  • 3m=174+24
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How we know Mac's age is 66 years old, we can identify Jess' age with the second equation:

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We replace the value of m:

  • j+66=87

And clear the variable j:

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In the end, Jess's age is 21 years old.

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3 years ago
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1 yard is 36 inches, so
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