Answer:
[tex]\angle 1 = 99^\circ[/tex]
[tex]\angle 3 = 99^\circ[/tex]
[tex]\angle 4 = 81^\circ[/tex]
Step-by-step explanation:
Given
[tex]\angle 2 = 81^\circ[/tex]
Required
Determine: [tex]\angle 1 . \angle 3 , \angle 4[/tex]
Solving for [tex]\angle 1[/tex], we have:
[tex]\angle 2 + \angle 1 = 180^\circ[/tex] --- angle on a straight line
So, we have:
[tex]\angle 1 = 180^\circ-\angle 2[/tex]
[tex]\angle 1 = 180^\circ-81^\circ[/tex]
[tex]\angle 1 = 99^\circ[/tex]
To solve for [tex]\angle 3, \angle 4[/tex], we have:
[tex]\angle 3 = \angle 1[/tex]
[tex]\angle 4 = \angle 2[/tex] --- Vertically opposite angles
So:
[tex]\angle 4 = 81^\circ[/tex]
[tex]\angle 3 = 99^\circ[/tex]
