Question

Find m∠Abc. (5x+3) (3x+7)

Answer 1

The angle is a right angle so ∠ABC and ∠CBD will add up to 90°. Let's find x first.

(5x + 3) + (3x + 7) = 90
Combine like terms.

8x + 10 = 90
Subtract 10 from both sides.

8x = 80
Divide both sides by 8.

x = 10
Plug in x into ∠ABC.

5(10) + 3 = 53
m∠ABC = 53°

Answer 2

Right off the bat, we can notice that Angle ABD is a right angle. This means that it must add up to 90 degrees. Therefore, we can write that:

`(5x+3)+(3x+7) = 90`

Let's combine like terms:

`8x+10=90`

Solve for x:

`8x=80`

`x = 10`

Now, since we need to find the measure of angle ABC which is given by (5x+3), we can plug the newly found value of x in to figure it out:

`5(10)+3 = 53`

Therefore, Angle ABC = 53°.