Question

1. fireworks the designers of a fireworks display want to have four fireworks travel along parallel trajectories. they decide to place two launchers on a dock and two launchers on the roof of a building. to make this display work correctly, what should the measure of angle 1 be? explain.
2. analyze problems chaska is making a giant letter a to put on the rooftop of the a is for apple orchard store. the figure shows a sketch of the design.

a. what should the measures of angles 1 and 2 be so the horizontal part of the a is truly horizontal? explain.
b. when building the a, chaska makes sure that angle 1 is correct, but when he measures angle 2, it is not correct. what does this imply about the a?

Explanation:

Step1: Use the property of supplementary angles

For the first part (question 16), since the trajectories are parallel and we assume a transversal (the line connecting the launchers), if the angle adjacent to angle 1 is \(30^{\circ}\), and they are supplementary (sum to \(180^{\circ}\)). So \(\angle1 = 180^{\circ}- 30^{\circ}\)

Step2: Calculate the value of \(\angle1\)

\(\angle1=150^{\circ}\)

For question 17a:

Step1: Use the property of supplementary angles for angle 2

Since the horizontal part is to be horizontal and we have an angle of \(108^{\circ}\) adjacent to angle 2. Using the supplementary - angle property (\(\angle2 + 108^{\circ}=180^{\circ}\)), we get \(\angle2=180^{\circ}-108^{\circ} = 72^{\circ}\)

Step2: Use the property of parallel lines (if we assume symmetry for the horizontal part of \(A\))

If the horizontal part is truly horizontal and we assume the two non - horizontal sides of \(A\) are symmetric with respect to the vertical line through the middle of the horizontal part. Then \(\angle1=\angle2 = 72^{\circ}\)

For question 17b:

Step1: Analyze the implication of \(\angle1

eq\angle2\)
If \(\angle1\) is correct (\(\angle1 = 72^{\circ}\)) and \(\angle2
eq72^{\circ}\), then the horizontal part of the \(A\) is not truly horizontal. Because for the horizontal part to be horizontal (assuming the two non - horizontal sides are symmetric in a way that when \(\angle1=\angle2\), the horizontal part is parallel to a reference horizontal line)

Answer:

1. \(\angle1 = 150^{\circ}\) (because it is supplementary to the \(30^{\circ}\) angle when considering parallel trajectories and a transversal).

17a. \(\angle1=\angle2 = 72^{\circ}\) (using the supplementary - angle property for \(\angle2\) with the \(108^{\circ}\) angle and assuming symmetry for the horizontal part of \(A\)).
17b. The horizontal part of the \(A\) is not truly horizontal.