Question

Three adjacent angles are at a point. The second angle is 20 degrees more than the first, the third angle is 20 degrees more that the second. Find the measurements of all three angles. Compare the expressions you used for the 3 angles and their combined expression.

Answer 1

x+(x+20)+(x+40)=180

Explanation:

Answer 2

100, 120 and 140 degrees

Explanation:

Firstly, we assign a value for the smallest of the angles. Meaning, let’s say that the smallest angle is x. The next angle would be x+20 since it is 20 degrees more than the first.

The third angle would be x+40 since this itself is 20 degrees more than the second

Now, Like we are made to know, these angles are at point. If we apply one of the fundamental laws of geometry, it states that the sum of angles at a point is 360. What this means is that if we add all the figures together, we get a total of 360 degrees.

This means x + x + 20 + x + 40 = 360

3x + 60 = 360

3x = 360-60

3x = 300

x = 300/3

x = 100 degrees

The second angle is x + 20 = 100+ 20 = 120

The third a x + 40 = 100 + 40 = 140

Hence, the angles are 100,120 and 140