In the given setup with parallel lines and a transversal, angles 1, 2, 3, and 4 are congruent, each measuring 120 degrees, following the properties of corresponding angles, vertically opposite angles, and the angle sum on a straight line.
In the given diagram, lines l, m, and n are parallel, and p is a transversal. It is noted that the angle sum on a straight line is 180 degrees, and specifically, angle 4 is given as 60 degrees. This implies that angle 4 on the straight line with 60 degrees results in angle 4 being 120 degrees.
As per the properties of parallel lines and transversals, corresponding angles are equal. Therefore, angle 1 is equal to angle 4, and angle 2 is also equal to angle 1 as lines l and m are parallel, and p serves as a transversal. Consequently, angle 1, angle 2, and angle 4 are all equal, each measuring 120 degrees.
Furthermore, according to the property of vertically opposite angles, angle 3 is equal to angle 2. Since angle 4 is established as 120 degrees, it follows that angle 3 is also 120 degrees.
To summarize, angle 1, angle 2, angle 3, and angle 4 are all congruent, each measuring 120 degrees, as determined through the given properties of parallel lines, transversals, and the angle sum on a straight line.
The question probable may be:
In the figure l , m and n are parallel lines intersected by transversal p at X , Y and Z respectively. Find angle 1 , 2 and 3.