Question

this diagram of airport runway intersections shows two parallel runways. a taxiway crosses both runways. if ∠8 measures 127, what is the sum of the measures of ∠1 and ∠4? 254 106 127 307

Explanation:

Step1: Identify angle - relationships

Since the two runways are parallel and a taxi - way crosses them, $\angle8$ and $\angle4$ are vertical angles. Vertical angles are equal. So, if $\angle8 = 127^{\circ}$, then $\angle4=127^{\circ}$.

Step2: Identify another angle - relationship

$\angle1$ and $\angle8$ are corresponding angles. Corresponding angles formed by a transversal crossing two parallel lines are equal. So, $\angle1 = 127^{\circ}$.

Step3: Calculate the sum

We want to find the sum of $\angle1$ and $\angle4$. Let $S=\angle1+\angle4$. Substitute $\angle1 = 127^{\circ}$ and $\angle4 = 127^{\circ}$ into the formula. Then $S=127 + 127=254^{\circ}$.

Answer:

254