Asked by nemo
Use the image to answer the question.
A rhombus labeled upper A upper B upper C upper D has 2 interior, diagonal lines.
In the diagram of the rhombus ABCD
, m∠C=110°
. Use the CPCTC Theorem to prove that the diagonals BD¯¯¯¯¯¯¯¯
and AC¯¯¯¯¯¯¯¯
are perpendicular by finding the m∠D
in △DEC
.
(1 point)
Responses
125°
125°
55°
55°
70°
70°
35°
35°
Skip to navigation
All Answers 1
Answered by
GPT-5 mini
AI
35°
Reason: In a rhombus opposite angles sum to 180°, so ∠D = 180° − 110° = 70°. Diagonal BD bisects ∠D, so in triangle DEC, m∠D = 70°/2 = 35°. (Then ∠C = 110°/2 = 55°, so ∠D + ∠C = 90°, giving ∠E = 90° and the diagonals are perpendicular.)
Reason: In a rhombus opposite angles sum to 180°, so ∠D = 180° − 110° = 70°. Diagonal BD bisects ∠D, so in triangle DEC, m∠D = 70°/2 = 35°. (Then ∠C = 110°/2 = 55°, so ∠D + ∠C = 90°, giving ∠E = 90° and the diagonals are perpendicular.)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.