Question

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 .

Answer 1

Answer:
x = 12

Step-by-step 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 :)