Question

1. the diagram shows three lines with some marked angle measures. find the missing angle measures marked with question marks. 4. describe a sequence of translations, rotations, and reflections that takes polygon p to polygon q. 5. point b has coordinates (-2,-5). after a translation 4 units down, a reflection across the y -axis, and a translation 6 units up, what are the coordinates of the image?

Explanation:

3.

Step1: Recall vertical - angle and supplementary - angle properties

Vertical angles are equal, and the sum of angles around a point is 360°, and supplementary angles add up to 180°.
For the first set of angles with 35°:
The angle vertical to 35° is 35°. The supplementary angles to 35° are 180 - 35=145°. So the four angles are 35°, 145°, 35°, 145°.
For the second set of angles with 27°:
The angle vertical to 27° is 27°. The supplementary angles to 27° are 180 - 27 = 153°. So the four angles are 27°, 153°, 27°, 153°.

Step1: Analyze the relative position of Polygon P and Polygon Q

First, translate Polygon P 4 units to the right. Then, rotate Polygon P 90° clockwise about a suitable center (for example, the bottom - left vertex of Polygon P).

Step1: First translation 4 units down

The original point B has coordinates (-2,-5). After translating 4 units down, the y - coordinate changes. The new coordinates are (-2,-5 - 4)=(-2,-9).

Step2: Reflection across the y - axis

When reflecting a point (x,y) across the y - axis, the x - coordinate changes sign. So, the new coordinates of (-2,-9) after reflection across the y - axis are (2,-9).

Step3: Second translation 6 units up

The y - coordinate of the point (2,-9) changes. The new coordinates are (2,-9 + 6)=(2,-3).

Answer:

For the first set of question - marks: 35°, 145°, 35°, 145°; for the second set of question - marks: 27°, 153°, 27°, 153°

4.