Given:
When the measure of ∠4 is 120°, the measure of ∠1 is 60°.
To determine:
The statement is always or sometimes true.
Solution:
If two lines are intersecting, then 4 angles are formed.
Sum of the measure of adjacent angles in a straight line is always 180°.
Let us substitute ∠4 = 120° and find ∠1.
m∠1 + m∠4 = 180°
m∠1 + 120° = 180°
Subtract 120° from both sides.
m∠1 + 120° - 120° = 180° - 120°
m∠1 = 60°
Therefore when the measure of ∠4 is 120°, the measure of ∠1 is 60°.
This statement is always true.