Question

what is the value of y? y =

Explanation:

Step1: Use the property of congruent triangles

Since \(MB\) is the perpendicular bisector of \(JK\), \(\triangle MJ B\cong\triangle MK B\) (by Hypotenuse - Leg congruence in right - angled triangles). So \(MJ = MK\).

Step2: Set up the equation

We are given \(MJ=8y - 30\) and \(MK = 2y\). Then \(8y-30=2y\).

Step3: Solve the equation for \(y\)

Subtract \(2y\) from both sides: \(8y-2y-30=2y - 2y\), which gives \(6y-30 = 0\).
Add \(30\) to both sides: \(6y-30 + 30=0 + 30\), so \(6y=30\).
Divide both sides by \(6\): \(y=\frac{30}{6}\).

Answer:

\(y = 5\)