Q:

# Which labeled angle has the greatest measure? The diagram is not to scale.

Accepted Solution

A:
C) < (angle) 3 has the greatest measure.
Why??
Because all angles of a triangle add up (sum) to 180°. Also the 3rd angle of the triangle, let's call it < 4 (not labeled) forms a line with < 3, thereby making < 4 + < 3 = 180. The angles that together make a straight line are called supplementary, meaning they sum to 180.
Therefore, we could say that:
< 1 + < 2 + < 4 = 180
And also that < 4 + < 3 = 180
So < 4 = 180 - < 3
Therefore < 1 + < 2 + (180 - < 3) = 180, by substitution.
And by dropping the () and adding < 3 to both sides, we get:
< 1 + < 2 + 180 - < 3 = 180
< 1 + < 2 + 180 - < 3 + < 3 = 180 + < 3
< 1 + < 2 + 180 = 180 + < 3
< 1 + < 2 +180 -180 = 180 + < 3 - 180
< 1 + < 2 = < 3
And now, by logic, we can see that the sum of two positive angles (1 and 2), if equal to another (3), then the individual value of either 1 or 2 has to be less than their sum (3).
So < 3 MUST be greater than either < 1 or < 2