In the accompanying diagram of rectangle abcd, latex: m\angle bac=3x+4 m ∠ b a c = 3 x + 4 and latex: m\angle acd=x+28 m ∠ a c d = x + 28 .

x = 12

Explanation:
In a rectangle, each two opposite sides are parallel.

Therefore, in rectangle ABCD:
AB would be parallel to CD

We know alternating angles formed within parallel lines are equal in measure.

In the given rectangle, we have:
∠ACD and ∠BAC are alternating angles, which means that they are equal.

Therefore:
∠ACD = ∠BAC
x + 28 = 3x + 4
28 - 4 = 3x - x
2x = 24
x = 12

We can check our solution:
∠ACD = 12 + 28 = 40°
∠BAC = 3(12) + 4 = 40°
They are equal

Hope this helps :)

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