Question

In triangle QRS, `/_Q` and `/_R` are congruent. The measure of `/_S` is three times the measure of `/_Q`. What is the measure of `/_S` in degrees?

Answer 1

`/_S=108°`

Explanation:

Let `/_Q=/_R=x`

`/_S=3x` because it is three times the measure of `/_Q`.

The sum of the interior angles of a triangle is `180°`.

`[1]" "/_Q+/_R+/_S=180°`

Plug in the values of the three angles.

`[2]" "x+x+3x=180°`

`[3]" "5x=180°`

Divide both sides by 5.

`[4]" "x=36°`

Now that you know what `x` is, you can get `/_S` by multiplying `x` by `3`.

`[1]" "/_S=3x`

Plug in the value of `x`.

`[2]" "/_S=3(36°)`

`[3]" "color(blue)(/_S=108°)`