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°