Use the image to answer the question.

Question

A rhombus labeled upper A upper B upper C upper D has 2 interior, diagonal lines.

In the diagram of the rhombus, m∠EDC=42°
and DE¯¯¯¯¯¯¯¯
is perpendicular to AC¯¯¯¯¯¯¯¯
. Using what you know about perpendicular bisectors of a rhombus, what is the m∠ECD
?

(1 point)
m∠ECD
is
°.
Remaining Attempts : 3
Skip to navigation

Answer 1

In a rhombus, the diagonals bisect each other at right angles. Since DE is perpendicular to AC, we can conclude that triangle EDC is a right triangle.

Given that \( m∠EDC = 42° \), we can find \( m∠ECD \) using the fact that the sum of angles in a triangle is \( 180° \).

Using the formula for the sum of angles in a triangle: \[ m∠EDC + m∠ECD + m∠DCE = 180° \] Since \( m∠E > m∠DCE \) and DE is perpendicular to AC, \( m∠DCE \) must also be \( 90° \): \[ m∠EDC + m∠ECD + 90° = 180° \]

Substitute the given angle: \[ 42° + m∠ECD + 90° = 180° \] \[ m∠ECD + 132° = 180° \] \[ m∠ECD = 180° - 132° \] \[ m∠ECD = 48° \]

Therefore, the measure of \( m∠ECD \) is \( 48° \).