Question

Set up a linear equation(s) that will help you to find a solution to the following problem: One angle of a triangle is twice as large as another angle. The measure of the third angle is 20 more than the measure of the smallest angle. Find the measure of each angle of the triangle.

Answer 1

remember
all angles add to 180

x+y+z=180
one is 2 times as another
x=2y
measure of 3rd angle (z) is 20 more than smalllest
since y has to be doubled to get x, y is smallest
z is 20 more than y
z=20+y


we have
x=2y
z=20+y
sub those
x+y+z=180
2y+y+20+y=180
4y+20=180
minus 20 both sides
4y=160
divide 4
y=40
sub back
x=2y
x=2(40)
x=80
z=20+y
z=20+40
z=60

the angles are
80 degrees, 40 degrees, 60 degrees