Question

vertical/adjacent/complementary angles (algebraic) unique id: 0056 score: 0/3 penalty: none question solve for the value of r. answer attempt 1 out of 2 r =

Explanation:

Step1: Identify angle relationship

The two angles $(5r + 8)^{\circ}$ and $(7r-8)^{\circ}$ are vertical angles. Vertical angles are equal. So we set up the equation $5r + 8=7r - 8$.

Step2: Solve the equation for r

Subtract $5r$ from both sides: $5r+8-5r=7r - 8-5r$, which simplifies to $8 = 2r-8$.
Then add 8 to both sides: $8 + 8=2r-8 + 8$, giving $16 = 2r$.
Divide both sides by 2: $\frac{16}{2}=\frac{2r}{2}$, so $r = 8$.

Answer:

$r = 8$