Question

Question #f6d65

Answer 1

22 and 158

Explanation:

Let `x` denote the value of the first angle

`x + 2x +114 = 180`

`=>3x+114-180`

`=>3x=66`

`=>x=22`

`=>2x+114=2*22+114=158`

Answer 2

Measure of the first angle (in degrees): `22`
Measure of the second angle (in degrees): `158`

Explanation:

Let's start by representing the first angle with the variable `x`. For the second angle, it will be `114` degrees larger `(+114)` than `2` times the measure of the first angle `(2x)`.

First angle `= x`
Second angle `= 2x+114`

We know the sum of both angles must be equal to `180` degrees, so we can make our equation now...

`x+2x+114= 180`

Combine like terms (`x` and `2x`) to get

`3x+114= 180`

Subtract `114` from both sides to get

`3x=66`

Divide both sides by `3` to isolate `x`. This gets us

`x=22`

It's important to realize what our solution for `x` means. We designated `x` as being equal to the measure of the first angle.

First angle `(x)= 22^@`
The second angle is `2x+114`, and since we know what `x` is, we can plug it in for this equation.

`2(22)+114= 44+114= 158`

Second angle `= 158^@`

To make sure our measures for the angles make sense, we just add them up and see if we get `180^@`.

`22^@+158^@ = 180^@`