Question #0fe9b

1 Answer
Sep 13, 2017

smaller angle=70
larger angle=110

Explanation:

Let us write this problem in terms of x and y:

  • where x is the smaller angle
  • and y is the larger angle

We know that the large angle (y) is equal to 30-2*the smaller angle(x)
#y=2*x-30#

Knowing also that the angle are supplementary,
#rarr x+y=180#

Substituting y by its value in terms of x we get:
#x+(2*x-30)=180#
#x+2*x-30=180#
#3*x-30=180#

Adding 30 to both sides of the equation to isolate the unknown's term:
#3*x cancel(-30) cancel(+30)=180+30#
#3*x=210#

Dividing both sides of equation by 3 to isolate x:
#(cancel(3)*x)/cancel3=210/3#
#x=70#

#y=2*x-30#
#y=2*70-30=140-30=110#