Question

find the value of y.
(3x + 45)°
63°
(7x - 7)°
(y - 9)°

Explanation:

Step1: Find the value of \(x\)

Since the two angles \((3x + 45)^{\circ}\) and \((7x-7)^{\circ}\) are equal (alternate - interior angles for parallel lines), we set up the equation \(3x + 45=7x-7\).
Subtract \(3x\) from both sides: \(45 = 4x-7\).
Add \(7\) to both sides: \(4x=45 + 7=52\).
Divide both sides by \(4\): \(x = 13\).

Step2: Find the value of \(y\)

We know that \((y - 9)+(3x + 45)=180\) (same - side interior angles for parallel lines).
Substitute \(x = 13\) into \(3x + 45\): \(3\times13+45=39 + 45=84\).
Then the equation becomes \(y-9+84 = 180\).
Simplify: \(y+75=180\).
Subtract \(75\) from both sides: \(y=180 - 75=105\).

Answer:

\(y = 105\)