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?

1 Answer
Dec 1, 2015

#/_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°)#