Question

solve for the value of k.
answer attempt 1 out of 2
k =

Explanation:

Step1: Use the angle - sum property

The sum of the angles \((2k - 2)^{\circ}\), \(90^{\circ}\), and \((k + 2)^{\circ}\) is \(180^{\circ}\) (a straight - line angle). So, \((2k-2)+90+(k + 2)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((2k-2)+(k + 2)+90=(2k + k)+(-2 + 2)+90\).
\(3k+0 + 90=180\), which simplifies to \(3k+90=180\).

Step3: Solve for \(k\)

Subtract 90 from both sides: \(3k+90-90=180 - 90\).
\(3k=90\).
Divide both sides by 3: \(k=\frac{90}{3}\).

Answer:

\(k = 30\)