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Two angles are complementary. The first angle is 2X degrees. The second angle is X +30° determine the larger angle

Respuesta :

texaschic101
complimentary angles, when added = 90 degrees

2x + x + 30 = 90
3x + 30 = 90
3x = 90 - 30
3x = 60
x = 60/3
x = 20

2x ..... 2(20) = 40
x + 30 ....20 + 30 = 50 <=== larger angle

Answer:

The larger angle is the second one, which is equal to 50°.

Step-by-step explanation:

Givens

  • The two angles are complementary. (This means the sum of them is equal to 90°, because they form a right angle)
  • The first angle is defined as [tex]2x[/tex] and the second angle is [tex]x+30[/tex].

So,

[tex]2x+x+30=90[/tex], because both angles must sum 90°, by defintion of complementary angles.

Then, we solve for [tex]x[/tex]

[tex]3x=90-30\\x=\frac{60}{3}\\ x=20[/tex]

Now, we substitue this value in each angle expression

First angle: [tex]2x=2(20)=40\°[/tex]

Second angle: [tex]x+30=20+30=50\°[/tex]

Therefore, the larger angle is the second one, which is equal to 50°.

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