Answer:
[tex]\angle 1+\angle 5 = 90[/tex]
Step-by-step explanation:
Given
The attached plot
Required
Prove that:
[tex]\angle 1+\angle 5 = 90[/tex] --- right angle
From the plot, we have:
[tex]\angle 1+\angle 2 + \angle 3+\angle 4+\angle 5 = 360[/tex] --- angle at a point
[tex]\angle 2+\angle 3 = 180[/tex] --- straight line
[tex]\angle 4 = 90[/tex] --- This divides [tex]\angle 2 + \angle 3[/tex] to equal parts
So, we have:
[tex]\angle 1+\angle 2 + \angle 3+\angle 4+\angle 5 = 360[/tex]
[tex]\angle 1+ (\angle 2 + \angle 3) +(\angle 4)+\angle 5 = 360[/tex]
This gives:
[tex]\angle 1+ 180 +90+\angle 5 = 360[/tex]
[tex]\angle 1+ 270+\angle 5 = 360[/tex]
Collect like terms
[tex]\angle 1+\angle 5 = 360-270[/tex]
[tex]\angle 1+\angle 5 = 90[/tex] --- proved
