2) ABCD is a rectangle, answer each question and explain how you get the a
Find the following measurements and explain how you get the answer.
MZABC =
Explain your reason (you can use the properties of rectangle to
explain your answer):
If AC=12, DE =
Your explanation:

m∠ABC = 90°, because the four angles are equal and their sum is 360°, then 360 ÷ 4 = 90°

DE = 6 units, because it is half DB which is equal to AC and AC = 12

m∠2 = 55°, because the sum of the measures of ∠1 and ∠2 is 90°

m∠4 = 75°, because it is equal m∠EAD and m∠2 in Δ AED which has ∠5

Step-by-step explanation:

Let us revise the properties of a triangle

∵ ABCD is a rectangle

∴ m∠ABC = 90°

m∠ABC = 90°, because the four angles are equal and their sum is 360°, then 360 ÷ 4 = 90°

∵ AC and BD are the diagonals of the rectangle

∴ AC = BD

∵ AC = 12 units

∴ BD = 12 units

∵ The two diagonals bisect each other

∴ E is the mid-point of AC and BD

∴ AE = EC = AC

∴ DE = EB = DB

∵ DB = 12 units

∴ DE =    × 12 = 6 units

DE = 6 units, because it is half DB which is equal to AC and AC = 12

∵ m∠D = 90° ⇒ property of rectangle

∵ m∠D = m∠1 + m∠2

∴ m∠1 + m∠2 = 90°

∵ m∠1 = 35°

∴ 35 + m∠2 = 90

- Subtract 35 from both sides

∴ m∠2 = 55°

m∠2 = 55°, because the sum of the measures of ∠1 and ∠2 is 90°

In Δ AED

∵ ED = EA ⇒ halves of equal diagonals are equal

∴ m∠EAD = m∠2 ⇒ base angles of an isosceles triangle

∵ m∠5 = 30°

- The sum of the interior angles of a triangle is 180°

∴ m∠2 + m∠2 + m∠5 = 180

∴ 2 m∠2 + 30 = 180

- Subtract 50 from both sides

∴ 2 m∠2 = 150

- Divide both sides by 2

∴ m∠2 = 75°

∴ m∠EAD = 75°

∵ AD // BC ⇒ opposite sides in a rectangle

∵ AC is a transversal

∴ m∠DAE = m∠4 ⇒ alternate angles

∴ m∠4 = 75°

m∠4 = 75°, because it is equal m∠EAD and m∠2 in Δ AED which has ∠5

step-by-step explanation:

most likely the answer is a.

alice wins if a total of 5 is rolled. finn wins if a total of 9 is rolled.

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.