Answer:
69 degrees
Step-by-step explanation:
1) Find x
The angles measured x degrees and (x-28) degrees have a sum of 180 degrees because straight lines always have a measure of 180 degrees. Knowing this, construct the equation:
[tex]x+x-28=180\\2x-28=180[/tex]
Add 28 to both sides
[tex]2x-28+28=180+28\\2x=208[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}= \frac{208}{2} \\x= 104[/tex]
Therefore, x is equal to 104 degrees.
2) Find the measure of the (x-28) degree angle
Plug x into x-28
[tex]x-28\\= 104-28\\= 76[/tex]
Therefore, the measure of this angle is 76 degrees.
3) Find y
All the interior angles in any triangle will add up to 180 degrees. Knowing this, we can construct another equation:
[tex](2y-1)+76+y= 180[/tex]
Open up the parentheses
[tex]2y-1+76+y= 180\\3y+75= 180[/tex]
Subtract both sides by 75
[tex]3y+75-75=180-75\\3y=105[/tex]
Divide both sides by 3
[tex]\frac{3y}{3}= \frac{105}{3} \\y=35[/tex]
Therefore, y is equal to 35 degrees.
4) Find the measure of the (2y-1) degree angle
Plug y into 2y-1
[tex]2y-1\\= 2(35)=1\\= 70-1\\= 69[/tex]
Therefore, y is equal to 69 degrees.
I hope this helps!
