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Alborosie
3 years ago
10

Find the measure of <_A. (show work if possible).

Mathematics
1 answer:
Sholpan [36]3 years ago
4 0

Answer:

<em>We </em><em>know </em><em>that </em><em>exterior </em><em>angle </em><em>of </em><em>a </em><em>triangle </em><em>is </em><em>equal </em><em>to </em><em>the </em><em>sum </em><em>of </em><em>two </em><em>opposite </em><em>interior </em><em>angle</em><em>.</em>

Step-by-step explanation:

<A = 4y

< B = 3y + 6°

<BCD = 111°

Now

<BCD = <A + <B( exterior angle of a triangle is equal to the sum of two opposite interior angle)

111° = 4y + 3y + 6°

111° - 6° = 7y

105° =7y

Therefore y = 15°

The measure of <A = 4*15°= 60°

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Multiply both sides of the second equation by 100 to get rid of the decimals:

0.05<em>n</em> + 0.10<em>d</em> = 1.50

==>  5<em>n</em> + 10<em>d</em> = 150

Multiply both sides of the first equation by -5:

<em>n</em> + <em>d</em> = 21

==>  -5<em>n</em> - 5<em>d</em> = -105

Add the two equations together:

(5<em>n</em> + 10<em>d</em>) + (-5<em>n</em> - 5<em>d</em>) = 150 + (-105)

Notice that the terms containing <em>n</em> get eliminated and we can solve for <em>d</em> :

(5<em>n</em> - 5<em>n</em>) + (10<em>d</em> - 5<em>d</em>) = 150 - 105

5<em>d</em> = 45

<em>d</em> = 45/5 = 9

Plug this into either original equation to solve for <em>n</em>. Doing this with the first equation is easiest:

<em>n</em> + 9 = 21

<em>n</em> = 21 - 9 = 12

So Donna used 12 nickels and 9 dimes.

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