Answer:
x = 15
y = 12
m < AED = 83°
m < DEC = 97°
Step-by-step explanation:
According to the given problem:
< AED = (6x - 7)°
< BEC = (4x + 23)°
< AEB = (8y + 1)°
< DEC = (5y + 37)°
Two angles are vertical angles if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent.
Given that < AED and < BEC are vertical angles, then it means that they have the same measure.
The same goes with < AEB and <DEC, they are also considered as vertical angles.
To solve for x:
< AED = < BEC
(6x - 7)° = (4x + 23)°
Subtract 4x from both sides:
6x - 4x - 7 = 4x - 4x + 23
2x - 7 = 23
Add 7 to both sides:
2x - 7 + 7 = 23 + 7
2x = 30
Divide both sides by 2 to solve for x:
2x/2 = 30/2
x = 15
To solve for y:
< AEB = <DEC
(8y + 1)° = (5y + 37)°
Subtract 5y from both sides:
8y - 5y + 1 = 5y - 5y + 37
3y + 1 = 37
Subtract 1 from both sides:
3y + 1 - 1 = 37 - 1
3y = 36
Divide both sides by 3 to solve for y:
3y/3 = 36/3
y = 12
To double check whether our values of x and y are correct, substitute these values into the established equality statements:
< AED = < BEC
(6x - 7)° = (4x + 23)°
[6(15) - 7]° = [4(15) + 23]°
(90 - 7)° = (60 + 23)°
83° = 83° (True statement. Therefore, x = 15 is the correct answer, and m < AED = 83°).
< AEB = <DEC
(8y + 1)° = (5y + 37)°
[8(12) + 1)° = [5(12) + 37]°
(96 + 1)° = (60 + 37)°
97° = 97° (True statement. Therefore, y = 12 is the correct answer, and m < DEC = 97°).
Please mark my answers as the Brainliest if you find this helpful :)
