Answer:
[tex]\angle 2 =145^\circ[/tex]
Step-by-step explanation:
Given
[tex]\angle 4 = 55^\circ[/tex]
Required
Find [tex]\angle 2[/tex]
From the attached image, we have:
[tex]\angle 5 = 90[/tex] --- right angle
So, we have:
[tex]\angle 5 +\angle 4 = 90 + \angle 4[/tex]
Substitute: [tex]\angle 4 = 55^\circ[/tex]
[tex]\angle 5 +\angle 4 = 90 + 55[/tex]
[tex]\angle 5 +\angle 4 = 145[/tex]
To solve for [tex]\angle 2[/tex], we have:
[tex]\angle 2 =\angle 5 +\angle 4[/tex] --- Vertically opposite angles
So:
[tex]\angle 2 =145^\circ[/tex]
