A diagram of airport runway intersections shows 2 parallel runways. A taxiway crosses both runways. If angle 8 measures 119, wwhat is the sum of the measures of angle 1 and 4?
I think that the answer is 238. Is this right?
No one's answering.
To determine the sum of angles 1 and 4, we need to consider the properties of intersecting lines and transversals. Let's break down the problem step by step:
1. Identify the intersecting lines: The intersecting lines in this scenario are the taxiway and the two parallel runways.
2. Identify the angle pairs: Angle 8, along with angles 1 and 4, form a set of corresponding angles. Corresponding angles are congruent when two parallel lines are intersected by a transversal.
3. Determine the measurement of angle 8: In the given information, angle 8 measures 119 degrees.
4. Use the properties of corresponding angles: Because angles 8, 1, and 4 are corresponding angles, we can conclude that both angles 1 and 4 have the same measure as angle 8, which is 119 degrees.
5. Find the sum of angles 1 and 4: The sum of angles 1 and 4 is equal to twice the measure of angle 8 since both angles are congruent. Therefore, the sum of angles 1 and 4 is 2 * 119 = 238 degrees.
So, your answer of 238 for the sum of angles 1 and 4 is correct.