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

Answer:

              $57.50$° is the measure of ∠$1$.

              $17.50$° is the measure of ∠$2$.

              $105$° is the measure of ∠$3$.

Step-by-step 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 ∠$3$.