Asvab word problem

Question

In triangle ABC, the degree measures of the three interior angles are in the ratio of 1:2:3. What is the difference in the degree measures between the largest and the smallest angle

Answer 1

the 1:2:3 proportion accounts for six parts, overall, into which 180 degrees are divided.

each one sixth equals 30 degrees, so the angles measure 30, 60 and 90 degrees, respectively.

therefore the difference between largest and smallest is 90 - 30, or sixty degrees.

Answer 2

The sum of the three interior angles of any triangle is 180.

 

The K be the proportionality constant.

 

 1*k + 2*k + 3*k = 180

6*k = 180

 k = 30

 

 The angles are 1*k=1*30=30, 2*k=2*30=60, 3*k=3*30=90.

 The difference between the largest and smallest is 90-30 = 60