[tex]\bf Step-by-step~explanation:[/tex]
We are given that BA is perpendicular to BD, so that must mean that m∠ABD is a right angle, or 90º. This means: (8x - 10) + (4x + 52) = 90º, since both of the angles add up to become a right angle. We have to solve for x in order to find m∠CBD.
PART 1
[tex]\bf Step~1:[/tex]
Equation: (8x - 10) + (4x + 52) = 90
Let's add the like values together first.
[tex]\bf 8x+4x=12x\\-10+52 = 42[/tex]
[tex]\bf 12x+42=90[/tex]
[tex]\bf Step~2:[/tex]
Let's subtract 42 from both sides of the equation to isolate the variable we are solving for, x. Our goal is to isolate it completely to get a value that is equal to x.
[tex]\bf12x+42(-42)=90(=42)\\12x=48[/tex]
[tex]\bf Step~3:[/tex]
Divide both sides by 12 to get our final answer for x.
[tex]\bf\frac{12x}{12} =x\\\\\frac{48}{12}= 4\\\\x=4[/tex]
PART 2
Now that we have x, we simply plug it into our equation for m∠CBD.
[tex]\bf Step~1:[/tex]
[tex]\bf4x+52\\4(4)+52[/tex]
[tex]\bf Step~2:[/tex]
Multiply 4 and add 52.
[tex]\bf 4*4=16\\16+52=68[/tex]
[tex]\large\boxed{\bf Our~final~answer: mCBD=68}[/tex]
