Question

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

Explanation:

Step1: Identify angle relationship

The two angles $(2r + 4)^{\circ}$ and $(r+5)^{\circ}$ are complementary (since they form a right - angle, $90^{\circ}$).
So, $(2r + 4)+(r + 5)=90$.

Step2: Combine like terms

$2r+r+4 + 5=90$, which simplifies to $3r+9 = 90$.

Step3: Isolate the variable term

Subtract 9 from both sides: $3r+9-9=90 - 9$, resulting in $3r=81$.

Step4: Solve for $r$

Divide both sides by 3: $\frac{3r}{3}=\frac{81}{3}$, so $r = 27$.

Answer:

$r = 27$