In the figure below, ABCD is a trapezium. AF and EC are straight lines.
Peishan wrote four statements to describe the figure.
Statement A: ∠AED=∠ABC\angle AED = \angle ABC
Statement B: ∠EDA=∠FDC\angle EDA = \angle FDC
Statement C: ∠ABC+∠ECB=180∘\angle ABC + \angle ECB = 180^\circ
Statement D: ∠DAB+∠ABC=180∘\angle DAB + \angle ABC = 180^\circ
Which of the following statements are true?

Work through it with AI →

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

6

1. Evaluate Statement B

Since AFAF and ECEC are straight lines intersecting at DD, ∠EDA\angle EDA and ∠FDC\angle FDC are vertically opposite angles. Therefore, ∠EDA=∠FDC\angle EDA = \angle FDC. Statement B is true.

2. Evaluate Statement C

In trapezium ABCDABCD, ABAB is parallel to DCDC. Since E,D,CE, D, C are collinear, ABAB is parallel to ECEC. ∠ABC\angle ABC and ∠ECB\angle ECB (which is the same as ∠BCD\angle BCD) are interior angles between parallel lines. Therefore, ∠ABC+∠ECB=180∘\angle ABC + \angle ECB = 180^\circ. Statement C is true.

3. Identify the correct option

Statements B and C are true. This corresponds to option (3).

Answer

B and C only (option 3)

AI analysis — may contain mistakes.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.

More questions on this topic

  1. 1In the figure, WXYZ is a trapezium and AXYB is a rhombus. XBC and XAZ are straight lines. WX // ZY, BC = BY, ∠XAB=82∘\angle XAB = 82^\circ…
  2. 2In the figure below, ABGF and BCDG are rhombuses. ∠ABF=31∘\angle ABF = 31^\circ, ∠CBG=40∘\angle CBG = 40^\circ and EF is parallel to…
  3. 3In the figure, PQ = PS and SRP is a straight line. Find ∠RQS\angle\text{RQS}. Ans: ___ ∘^\circ
  4. 43.76°= 度 分 秒.
  5. 5In the figure below, WPRT is a square. QWU and SWV are straight lines. ∠QWP=13∘\angle QWP = 13^\circ and ∠TWS=28∘\angle TWS = 28^\circ…