Question

Please just answer this and explain how to solve...i’m not grasping the work :/

Answer 1

$\bf Step-by-step~explanation:$

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

$\bf Step~1:$

Equation: (8x - 10) + (4x + 52) = 90

Let's add the like values together first.

$\bf 8x+4x=12x\\-10+52 = 42$

$\bf 12x+42=90$

$\bf Step~2:$

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.

$\bf12x+42(-42)=90(=42)\\12x=48$

$\bf Step~3:$

Divide both sides by 12 to get our final answer for x.

$\bf\frac{12x}{12} =x\\\\\frac{48}{12}= 4\\\\x=4$

PART 2

Now that we have x, we simply plug it into our equation for m∠CBD.

$\bf Step~1:$

$\bf4x+52\\4(4)+52$

$\bf Step~2:$

Multiply 4 and add 52.

$\bf 4*4=16\\16+52=68$

$\large\boxed{\bf Our~final~answer: mCBD=68}$