Lines AN and CT are perpendicular. If mAFT = 3x + 21 and m CFN = y + 45, which is the value of x + y
To find the value of x + y, we need to use the fact that Lines AN and CT are perpendicular.
When two lines are perpendicular, the angles formed are right angles, which means they measure 90 degrees.
In this case, we have two angles: angle AFT (mAFT) and angle CFN (mCFN). According to the given information, mAFT = 3x + 21 and mCFN = y + 45.
Since lines AN and CT are perpendicular, angle AFT and angle CFN are right angles, and thus their measures are 90 degrees.
So, we can write the following equations:
3x + 21 = 90 (equation 1)
y + 45 = 90 (equation 2)
Now, we can solve these equations to find the values of x and y.
From equation 1:
3x + 21 = 90
Subtract 21 from both sides:
3x = 90 - 21
3x = 69
Divide both sides by 3:
x = 23
From equation 2:
y + 45 = 90
Subtract 45 from both sides:
y = 90 - 45
y = 45
Finally, we can find the value of x + y:
x + y = 23 + 45
x + y = 68
So, the value of x + y is 68.