Question

vertical/adjacent/complementary angles (algebraic)
score: 4/5 penalty: 0.25 off
question
solve for the value of k.
answer attempt 1 out of 2
k =

Explanation:

Step1: Recall angle - sum property

The sum of the angles in the given figure is 180° since they form a straight - line. So, $(2k - 2)^{\circ}+90^{\circ}+(k + 2)^{\circ}=180^{\circ}$.

Step2: Simplify the left - hand side

Combine like terms: $(2k-2 + k + 2)+90=180$. This simplifies to $3k+90 = 180$.

Step3: Isolate the variable term

Subtract 90 from both sides: $3k+90 - 90=180 - 90$, which gives $3k=90$.

Step4: Solve for k

Divide both sides by 3: $\frac{3k}{3}=\frac{90}{3}$, so $k = 30$.

Answer:

$k = 30$