Answer:
Measure of one angle is required.
Step-by-step explanation:
Kindly refer to the image attached.
AM and BN are the two parallel lines cut by a transversal PQ.
The angles formed are:
[tex]\angle 1, \angle 2, \angle 3, \angle 4, \angle 5, \angle 6, \angle 7 \ and\ \angle 8[/tex].
Let, only one of the angles is known to us.
Let, it is given that [tex]\angle 2 = 60^\circ[/tex]
AM is a straight line, therefore
[tex]\angle 1+\angle 2 =180^\circ\\\Rightarrow \angle 1 =180-60=120^\circ[/tex]
[tex]\angle 1[/tex] and [tex]\angle 3[/tex] are vertically opposite angles, therefore must be equal to each other.
[tex]\angle 1 = \angle 3 = 120^\circ[/tex]
[tex]\angle 2[/tex] and [tex]\angle 4[/tex] are vertically opposite angles, therefore must be equal to each other.
[tex]\angle 2 = \angle 4 = 60^\circ[/tex]
By Corresponding angle postulate, we can see the following:
[tex]\angle 2=\angle 5 =60^\circ\\\angle 3=\angle 6 =120^\circ\\\angle 1=\angle 8 =120^\circ\\\angle 4=\angle 7 =60^\circ[/tex]
Therefore, by knowing just one angle, all the angles can be found.
