Question

In a 90° angle there are two measures, m ∠ 1 = 3x° and m ∠ 2 = (x + 14)°

What are the angle measures?

Answer 1

Explanation:

We know that the two angles sum to be
`90`°, so we can write an equation that adds them together to solve for
`x`:

`(3x) + (x + 14) = 90`

`3x + x + 14 = 90`

`4x + 14 = 90`

`4x = 76`

`x = 19`

Now we know that
`x = 19`, so we can plug that into the two given angle measures:

`3x`

`3(19)`

`57`°

`(x + 14)`

`19 + 14`

`33`°

Answer 2

x = 19

∠ 1 = 57

∠ 2 = 33

Explanation:

Since there are 3 numbers that means that its a triangle. The equation will equal 180 because the sum of all angles of a triangle is 180. The equation is:

90 + 3x + x + 14 = 180

Subtract the 90 and 14 so that only the x's are left on the left.

3x + x + 14 = 90

3x + x = 76

Then, combine like terms:

4x = 76

Then, divide:

76/4 = 19

This is our x. But we need to find our angle measures. To do that, we replace the x's with 19.

∠ 1: 3(19) = 57

∠ 2: ((19) + 14) = 33

To check your answer, add all numbers and see if it adds up to 180:

90 + 57 + 33 = 180

180 = 180 ✔