Question

Call the three angles of a triangle ∠1,∠2,∠3

The measure of ∠2 is forty degrees less than that of ∠1; the measure of ∠3 is ten degrees less than twice that of ∠1If x is the measure of ∠1, then which of the following equations would we need to solve in order to calculate the measures of the angles?

Answer 1

`57.50`° is the measure of ∠
`1`.

`17.50`° is the measure of ∠
`2`.

`105`° is the measure of ∠
`3`.

Explanation:

Given that,

`x` is the measure of ∠
`1`.

Now,

The measure of ∠
`2` is forty degree less than that of ∠
`1`, so (
`x-40`) is the measure of ∠
`2`.

The measure of ∠
`3` is ten degree less than twice that of ∠
`1`, so (
`2x-10`) is the measure of ∠
`3`.

So,

According to Angle sum property,

Sum of the measures of the three angle of triangle is
`180`°.

Now,

∠
`1` + ∠
`2` + ∠
`3` =
`180`°

(
`x`) + (
`x-40`) + (
`2x-10`) =
`180`°

`4x - 50 = 180`°

`4x = 230`°

`x = 57.50`°

So,

`57.50`° is the measure of ∠
`1`.

`17.50`° is the measure of ∠
`2`.

`105`° is the measure of ∠
`3`.