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VLD [36.1K]
2 years ago
13

What is m<efh =(5×+1)°,m<hfg =62° and m <efg = (18×+11)°, find each measure.​

Mathematics
1 answer:
Naddik [55]2 years ago
6 0

Answer:

m\angle efg=21\°\\\\m\angle hfg=62\°\\\\m\angle efg=83\°

Step-by-step explanation:

Given:

m\angle efh=5x+1\\m\angle hfg=62\\m\angle efg=18x+11

Now, from the figure shown below,

The sum of angle efh and angle hfg is equal to the angle efg. This is true because of the angle addition postulate which states that when two angles are formed with the same vertex and different sides, then their sum is equal to the total angle made by both the sides at the vertex.

Here, point 'f' is the vertex and the sides are 'ef and 'fg'.

Therefore,

m\angle efh+m\angle hfg=m\angle efg

Plug in their values and solve for 'x'. This gives,

5x+1+62=18x+11\\5x+63=18x+11\\18x-5x=63-11\\13x=52\\x=\frac{52}{13}=4

Therefore, the angle measure of each are:

m\angle efg=5x+1=5(4)+1=20+1=21\°\\\\m\angle hfg=62\°\\\\m\angle efg=18x+11=18(4)+11=72+11=83\°

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<span>The<u> correct answer</u> is:

153/200.

Explanation<span>:

The amount for the first 6 months is 76500 and the amount for the last 6 months is 100000. This makes the ratio 76500/100000.

Both of these end with two 0's; this means they are both divisible by 100. 76500/100 = 765 and 100000/100 = 1000; this makes the ratio 765/1000.

Since these end with a 5 or a 0, they are divisible by 5; 765/5 = 153 and 1000/5 = 200; this makes the ratio 153/200.

153 is only divisible by 3 or 9; 153/3 = 51 and 153/9 = 17. None of these will divide evenly into 200, so we stop at 153/200.</span></span>
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