PLS HELP! Shannon is designing a new rectangular
flag for the school's color guard and is determining the
angles at which to cut the fabric. She wants the measure of
22 to be three times as great as the measure of Z1. She
thinks the measures of 23 and 24 should be equal. Finally,
she wants the measure of 26 to be half that of 25.
Determine the measures of the angles.
3

Step-by-step explanation:

Shannon is designing a rectangular flag.

Therefore, all the interior angles of this flag measure 90°.

m∠1 + m∠2 = 90°

Since, ∠2 is 3 times as great as the measure of ∠1.

m∠2 = 3(m∠1)

Therefore, m∠1 + 3(m∠1) = 90°

4(m∠1) = 90°

m∠1 = 22.5°

m∠2 = 3(m∠1)

        = 3(22.5)°

        = 67.5°

m∠3 + m∠4 = 90° [Interior angle of a rectangle]

She thinks ∠3 and ∠4 are equal,

m∠3 = m∠4

m∠3 + m∠3 = 90°

2m∠3 = 90°

m∠3 = 45°

m∠4 = m∠3 = 45°

m∠2 = m∠6 [Opposite angles of a parallelogram are equal]

Therefore, m∠2 = m∠6 = 67.5°  

Finally she wants the measure of ∠6 is half of the measure of ∠5.

m∠6 = (m∠5)

67.5° = (m∠5)

m∠5 = 2(67.5)°

        = 135°

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: