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german
3 years ago
13

Hi, is there anyone that could explain this?

Mathematics
1 answer:
DiKsa [7]3 years ago
3 0

Answer:

x° = 50°

Step-by-step explanation:

Since all angels on a triangle add up to 180°, we can start from there. We also can see since both angles have the exact same measurements, angle x and the unnamed angle must measure to the same degrees. We can now do 180° - 80° = 100° That leaves the two mystery angles at 100°/2 = 50°.

Therefore, x° = 50°.

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The measures of two complementary angles have a ratio of 3 : 2. What is the measure of the larger angle?
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<em>Question:</em>

The measures of two complementary angles have a ratio of 3 : 2. What is the measure of the larger angle?

—————

<em>Solution:</em>

Call those two angles  x  and  y, where  x  is the larger one.

If they are complementary, then their sum equals  90°:

x + y = 90°      (i)


Also, the ratio between  x  and  y  is  3 : 2, so

  x           3
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Product of the extremes = product of the means:

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Now, just solve this system of equations:

  x  +  y = 90°         (i)
2x – 3y =   0          (ii)


Solve it with elimination. Since you want to know the value of the larger angle, which is  x, then eliminate the variable  y  by doing the following:

Multiply the equation  (i)  by  3,

3x + 3y = 270°        (iii)
2x – 3y =     0          (ii)


then add both equations, so you cancel out the variable  y:

3x + 2x + 3y – 3y = 270° + 0

3x + 2x = 270°

5x = 270°

         270°
x  =  ———
           5

x = 54°    <———  this is the measure of the larger angle.


I hope this helps. =)


Tags:  <span><em>system of linear equations elimination method solve complementary angles algebra geometry</em>
</span>
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