Answer:
[tex]\angle 4 = 115^{\circ}[/tex]
[tex]\angle 3 = 65^{\circ}[/tex]
[tex]\angle 7 = 65^{\circ}[/tex]
Step-by-step explanation:
Given
[tex]\angle 2 = 65^{\circ}[/tex]
See attachment
Solving (a): [tex]\angle 4[/tex]
To solve for [tex]\angle 4[/tex], we make use of:
[tex]\angle 2 +\angle 4 = 180^{\circ}[/tex]
The relationship between both angles is that they are complementary angles
Make [tex]\angle 4[/tex] the subject
[tex]\angle 4 = 180^{\circ} - \angle 2[/tex]
Substitute [tex]65^{\circ}[/tex] for [tex]\angle 2[/tex]
[tex]\angle 4 = 180^{\circ} - 65^{\circ}[/tex]
[tex]\angle 4 = 115^{\circ}[/tex]
Solving (b): [tex]\angle 3[/tex]
To solve for [tex]\angle 3[/tex], we make use of:
[tex]\angle 3 =\angle 2[/tex]
The relationship between both angles is that they are complementary angles
[tex]\angle 3 = 65^{\circ}[/tex]
Solving (c): [tex]\angle 7[/tex]
To solve for [tex]\angle 7[/tex], we make use of:
[tex]\angle 7 = \angle 3[/tex]
The relationship between both angles is that they are alternate exterior angles.
So:
[tex]\angle 7 = 65^{\circ}[/tex]
