If ABCD is a rectangle and the measurement of angle CBD=47 what is the value of x

Accepted Solution

Answer: Option C.Step-by-step explanation: Observe the figure attached. The sum of the angles ∠b and 47° is 90 degrees. (They are complementary angles). Then the measure of ∠b is: [tex]b+47\°=90\°\\b=43\°[/tex] By definition, the diagonals of a rectangle are congruent. Therefore, the triangles formed when they intersect each other are isosceles triangles. Therefore: ∠b=∠a=43° By definition, the sum of the interior angles of a  triangle is 180 degrees. Then, you can calculate the value of x as following: [tex]x+b+a=180\°[/tex] Solve for x, then the result is: [tex]x=180\°-43\°-43\°\\x=94\°[/tex]