Question

question
solve for the value of k.

answer attempt 1 out of 2
k =

Explanation:

Step1: Identify angle sum

The angles around a point on a straight line (or forming a right - related set) here: the right angle is \(90^{\circ}\), and the two angles \((k + 2)^{\circ}\) and \((2k-2)^{\circ}\) along with the right angle should sum to \(180^{\circ}\) (since they are on a straight line). Wait, actually, looking at the diagram, the right angle, \((k + 2)^{\circ}\) and \((2k - 2)^{\circ}\) form a straight line? Wait, no, the right angle is \(90^{\circ}\), and the two angles \((k + 2)^{\circ}\) and \((2k-2)^{\circ}\) should add up to \(90^{\circ}\)? Wait, no, let's re - examine. The diagram has a right angle (the square), and two angles \((k + 2)^{\circ}\) and \((2k-2)^{\circ}\) such that \((k + 2)+(2k - 2)=90\)? Wait, no, maybe the sum of \((k + 2)^{\circ}\), the right angle (\(90^{\circ}\)) and \((2k-2)^{\circ}\) is \(180^{\circ}\)? Wait, no, actually, the two angles \((k + 2)^{\circ}\) and \((2k-2)^{\circ}\) are complementary to the right angle? Wait, no, let's think again. If we have a straight line, the sum of angles on a straight line is \(180^{\circ}\). The right angle is \(90^{\circ}\), and the other two angles \((k + 2)^{\circ}\) and \((2k-2)^{\circ}\) should add up to \(90^{\circ}\)? Wait, no, let's do the math. Let's assume that \((k + 2)+(2k - 2)=90\). Simplify the left - hand side: \(k + 2+2k-2 = 3k\). So \(3k=90\), then \(k = 30\)? Wait, no, maybe the sum of \((k + 2)\) and \((2k-2)\) is equal to \(90\) because of the right angle. Let's check:
\((k + 2)+(2k-2)=k + 2+2k-2=3k\). If \(3k = 90\), then \(k = 30\). Wait, let's verify. If \(k = 30\), then \((k + 2)=32^{\circ}\), \((2k-2)=58^{\circ}\), and \(32 + 58=90^{\circ}\), which matches the right angle. So the equation is \((k + 2)+(2k - 2)=90\).

Step2: Solve the equation

Simplify the left - hand side of the equation \((k + 2)+(2k-2)=90\):
\(k+2 + 2k-2=3k\)
So we have \(3k=90\)
Divide both sides by 3: \(k=\frac{90}{3}=30\)

Answer:

\(k = 30\)