Answer:
(Angle DBE) ∠DBE = 50°
Step-by-step explanation:
It is crucial for us to be able to interpret plane geometry related question in order to solve them efficiently.
From the question given; we have analysed and come up with a diagrammatic expression and mathematical solution that clearly explains the question .
Given that
BC and DF are parallel lines.
B is a point on AD
B is a point on AD
BD=BE
work out angle DBE and give a reason.
The diagram can be seen in the attached image below.
SInce ∠BD = ∠DE
Then triangle BDE is an isosceles triangle. In an isosceles triangle ; two sides are equal in length.
The sum of angles in an isosceles triangle = 180° (sum of angles in a triangle)
So;
∠BDE + ∠BED + ∠DBE = 180° (sum of angles in a triangle)
From the diagram; we will see that ∠ABC = ∠BDE (corresponding angle)
Since ; ∠ABC is not given and which is needed to solve this question.
Let's just assume that ∠ABC is 65° , the main thing is to be able to interpret and understand the concept of the question.
Now;
Since
∠ABC = ∠BDE
∠ABC = 65°
∠BDE = 65°
Again;
∠BDE + ∠BED + ∠DBE = 180° (sum of angles in a triangle)
∠BDE will be aso equal to ∠BED ; this is because since the length of the opposite sides of the isosceles triangle are equal, their angles will also be equal.
Therefore;
65° + 65° + ∠DBE = 180° (sum of angles in a triangle)
130 ° + ∠DBE = 180° (sum of angles in a triangle)
∠DBE = 180° - 130°
∠DBE = 50°
