Question

I can’t understand 21-23 can someone solve or explain them please (geometry)

Answer 1

21. <DBE and <ABE are both equal halves of <ABD, so in this case, m<ABE = m<DBE, so all you have to do is solve the equation:

6x + 2 = 8x - 14
add 14 to both sides, subtract 6x from both sides.
16 = 2x
Divide both sides by two. The solution is x = 8. To find m<ABE, replace x with 2, so your final answer is 14. m<ABE = 14

22. From what we know from 21, m<ABE = m<EBD, so keep that in mind. We still have to solve for m<EBD. Since one line is 180 degrees, we are able to write out this equation using the information given:

180 = 9x - 1 (m<ABE) + 9x - 1 (m<EBD) + 24x + 14 (m<DBC)
simplify this:
180 = 12 + 42x
subtract 12 from both sides, then divide by 42.
4 = x
Now we plug this in.
4 × 9 = 36. 36 - 1 = 35.
m<EBD = 35

23. From the past two equations, we know m<ABE consistently equals m<EBD. This means that, if they are bisectors of a right angle, they both equal 45 degrees. here is our equation:

45 = 13x - 7.
we add seven to both sides and divide by 13.
4 = x