Answer:
x = 36°
Step-by-step explanation:
Please check the labels in the image attached.
In vertex A, the sum of the angles in the line AB is 180°, so we have:
[tex]x + 90 + mA = 180[/tex]
[tex]mA = 90 - x[/tex]
The angle mCHB is a right angle, so the angle mAHB is also a right angle.
Then, using the internal angles of triangle AHB, we have:
[tex]mA + mAHB + mABH = 180[/tex]
[tex]90 - x + 90 + mABH = 180[/tex]
[tex]mABH = x[/tex]
Then, in vertex B, we have the sum of angles in the line BC equal to 180°:
[tex]3x + mABH + x = 180[/tex]
[tex]3x + x + x = 180[/tex]
[tex]5x = 180[/tex]
[tex]x = 180/5 = 36\°[/tex]
