Question

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 ∠2 to be three times as great as the measure of ∠1. She thinks the measures of ∠3 and ∠4 should be equal. Finally, she wants the measure of ∠6 to be half that of ∠5. Determine the measures of the angles.

Answer 1

To determine the measures of the angles, assign variables to each angle and translate the given information into equations. Substitute the given equations into the equation representing the sum of the angles, and solve for the angles.

Step-by-step explanation:

To determine the measures of the angles, let's assign variables to each angle: ∠1, ∠2, ∠3, ∠4, ∠5, and ∠6. Now, let's translate the given information into equations:

∠2 = 3∠1

∠3 = ∠4

∠6 = ∠5/2

Since the sum of the angles of a rectangle is 360 degrees, we can write the equation: ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 = 360

Now, we can substitute the given equations into the last equation and solve for the angles:

1. Substitute ∠2 = 3∠1 into the equation
2. Substitute ∠3 = ∠4 into the equation
3. Substitute ∠6 = ∠5/2 into the equation
4. Simplify and solve the resulting equation to find the values of the angles.

Once you solve the equations, you will find the measures of all the angles.