75 POINTS!!! WILL MARK BRAINLIEST!!! Find the measure of angle LNM
2 answers:
<em>m∠LNM = 54°</em>
<u><em>Here is why:</em></u>
In this photo there are two important angles with very important features, a central angle and an inscribed angle.
A central angle is an angle that is in the center of the circle, so angle P is a central angle. The arc that is associated with this angle is going to be the same measure as the central angle. I have labeled this in the photo below as <u>blue</u>.
An inscribed angle is an angle that lies on the circle, so angle N is an inscribed angle. The arc that is associated with this angle will be double the amount of the inscribed angle, or the angle is half of the measure of the arc. I have labeled this in the photo below as <u>red</u>.
Since we know that the central angle is 108°, with what we know about central angles we know that arc LM is going to be 108° as well.
We also know that an inscribed angle is half the amount of the arc so...
108 ÷ 2 = 54
<em><u>m∠LNM = 54°</u></em>
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Answer:
There are 72 dimes having a total value of $7.2.
Step-by-step explanation:
Let the number of dimes be 'd', nickels be 'n' and quarters be 'q'.
Given:
Number of dimes is three times quarters
Number of nickels is four less than twice the number of dimes.
Total amount in the piggy bank is $20.20
Now, as per question:
Number of dimes is three times quarters
Framing in equation form, we get:
Number of nickels is four less than twice the number of dimes.
Framing in equation form, we get:
Now, value of 1 dime in dollars is 0.1.
Value 'd' dimes = $0.1d ----------(A)
Value of 1 quarter = $0.25
Value of 'q' quarters = $0.25q ----------(B)
Value of 1 nickel = $0.05
Value of 'n' nickels = $0.05n ----------(C)
Now, total amount is equal to the sum of all the amounts of each type of coin.
So, adding equations (A), (B) and (C) and equating to 20.20, we get:
Now, using equations (1) and (2), the above equation can be rewritten as:
So, there are 72 dimes in the piggy bank.
Total value of 72 dimes = 72(0.1) = $7.2