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(12x)/(12) =x\\\\(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}`