Question

In triangle ABD, BE ⊥ AD and ∠EBD ≅ ∠CBD.

If ∠ABE = 52°, what is the measure of ∠EDB?
A) 12°
B) 26°
C) 52°
D) 64°

Answer 1

B.
`26^(\circ)`

Explanation:

We are given that a triangle ABD, BE is perpendicular to AD and angle EBD is congruent to angle CBD.

`\angleABE=52^(\circ)`

We have to find the measure of angle EDB.

Let
`\angle EBD=x`

Then,
`\angle CBD=x` because angle EBD is congruent to angle CBD.

`\angle ABE+\angle EBD+\angle CBD=180^(\circ)` (linear sum)

`52+x+x=180`

`2x=180-52=128`

`x=(128)/(2)=64^(\circ)`

In triangle EBD

`\angle BED=90^(\circ)`

`\angle EBD=64^{\circ]`

`\angle EBD+\angle BED+\angle EDB=180^(\circ)` (sum of angles of triangle )

Substitute the values then we get

`64+90+\angle EDB=180`

`154+\angle EDB=180`

`\angle EDB=180-154=26^(\circ)`

Hence,
`m\angle EDB=26^(\circ)`

Answer 2

Option B.
`26\°`

Explanation:

step 1

Find the measure of angle EBD

we know that

`m<EBD+m<CBD+m<ABE=180\°`

remember that

`m<EBD=m<CBD`

`m<ABE=52\°`

substitute the values

`2m<EBD+52\°=180\°`

`2m<EBD=180\°-52\°`

`m<EBD=128\°/2=64\°`

step 2

Find the measure of the angle EDB

we know that

The sum of the internal angles of a triangle must be equal to 180 degrees

In the right triangle BED

`m<EBD+m<BED+m<EDB=180\°`

we have

`m<EBD=64\°`

`m<BED=90\°`

substitute

`64\°+90\°+m<EDB=180\°`

`m<EDB=180\°-(64\°+90\°)=26\°`