Question

Please Show Work.

Angles A and B create a 120° angle. ∠A=3x+5 and ∠B=2x+15. Find the measures of both angles.

Answer 1

Answers:

x = 20

angle A = 65 degrees

angle B = 55 degrees

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Work Shown:

A+B = 120

(3x+5) + (2x+15) = 120

5x+20 = 120

5x = 120-20

5x = 100

x = 100/5

x = 20

Use this to find both angles

angle A = 3x+5 = 3(20)+5 = 65 degrees

angle B = 2x+15 = 2(20)+15 = 55 degrees

Then note how A+B = 65+55 = 120 to help confirm our answers.

Answer 2

`\huge\boxed{\angle A = 65, \angle B = 55}`

Explanation:

We can treat each of these angle equations as if they are the real angle measures.

We know these angles add up to 120°, so we can create an addition statement:

`(3x+5) + (2x+15) = 120`

We can then solve for x.

• Combine like terms:
  `5x + 20 = 120`
• Subtract 20 from both sides:
  `5x = 100`
• Divide both sides by 5:
  `x = 20`

Now that we know x = 20, we can substitute it into both equations for each angles and find it.

∠A =
`3x+5\\ 3 \cdot 20 + 5\\60+5\\65`

∠B =
`2x+15\\2\cdot 20 + 15\\ 40+15\\55`

We can test that this is right because 65+55 = 120.

Hope this helped!