If ABCD is a rectangle, and m_ADB = 55°, what is the value of x? A. 80 O B. 90 O C. 40 O D. 70 O E. 110​

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Explanation:

Label a new point E at the intersection of the diagonals. The goal is to find angle CEB. Notice how angle AED and angle CEB are vertical angles, so angle AED is also x.

Recall that any rectangle has each diagonal that is the same length, and each diagonal cuts each other in half (aka bisect). This must mean segments DE and AE are the same length, and furthermore, triangle AED is isosceles.

Triangle AED being isosceles then tells us that the base angles ADE and DAE are the same measure (both being 55 in this case).

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To briefly summarize so far, we have these interior angles of triangle ADE

For any triangle, the three angles always add to 180, so,

A+D+E = 180

55+55+x = 180

110+x = 180

x = 180-110

x = 70