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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°

In triangle ABD, BE ⊥ AD and ∠EBD ≅ ∠CBD. If ∠ABE = 52°, what is the measure of ∠EDB-example-1
User BeemerGuy
by
8.0k points

2 Answers

2 votes

Answer:

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)

User Emme
by
8.6k points
1 vote

Answer:

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\°

User Hooke
by
8.1k points