Answer:
[tex]x = 36^o[/tex]
Step-by-step explanation:
Given
See attachment
Required
Find x
First, calculate [tex]\angle BAH[/tex]
[tex]\angle BAH + 90 + x = 180[/tex] --- angle on a straight line
Collect like terms
[tex]\angle BAH = 180 -90-x[/tex]
[tex]\angle BAH = 90-x[/tex]
Next, calculate [tex]\angle HBA[/tex]
[tex]\angle HBA + x + 3x = 180[/tex] --- angle on a straight line
[tex]\angle HBA + 4x = 180[/tex]
Rewrite as:
[tex]\angle HBA = 180-4x[/tex]
[tex]\triangle HBA[/tex] is right-angled;
So:
[tex]\angle HBA + \angle BAH + 90 = 180[/tex]
This gives:
[tex]180 - 4x + 90 - x+ 90 = 180[/tex]
Collect like terms
[tex]- 4x - x = 180 - 180 - 90 - 90[/tex]
[tex]- 5x = -180[/tex]
Divide both sides by -5
[tex]x = 36^o[/tex]
