Question

4 lines extend from point B. A line extends straight up from B to point A. Another line extends up and to the right to point C. Another line extends slight up and to the right to point D. The other line extends slightly down and to the right to point E.
Given that ∠ABC ≅ ∠DBE, which statement must be true?

∠ABC ≅ ∠ABD
∠ABD ≅ ∠CBE
∠CBD ≅ ∠DBE
∠CBD ≅ ∠ABC

Answer 1

Answer:

The Correct Answer Is: ∠ABD ≅ ∠CBE

Step-by-step explanation:

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Answer 2

∠ABD≅∠CBE is the true statement of congruent angles as per the given condition ∠ABC ≅∠DBE.

What are congruent angles?

" Congruent angles are pair of such angles which are equal in their measurements."

According to the question,

Given,

∠ABC ≅∠DBE                                    ________(1)

As shown in the diagram drawn as per the given conditions we have,

'D' is the interior point of angle ABC.

Therefore,

∠ABC = ∠ABD + ∠CBD                         ______(2)

'C' is the interior point of ∠DBE.

Therefore,

∠DBE = ∠CBD + ∠CBE                              ______(3)

Substitute  (2) and (3) in (1) to represent congruent angles we get,

∠ABD + ∠CBD  ≅ ∠CBD + ∠CBE      

⇒∠ABD   ≅  ∠CBE                            (∠CBD is common in both)

Hence, ∠ABD≅∠CBE is the true statement of congruent angles as per the given condition ∠ABC ≅∠DBE.

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