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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 A 12 B 26 C 52 D 64 class=

Respuesta :

calculista

Answer:

Option B. [tex]26\°[/tex]

Step-by-step explanation:

step 1

Find the measure of angle EBD

we know that

[tex]m<EBD+m<CBD+m<ABE=180\°[/tex]

remember that

[tex]m<EBD=m<CBD[/tex]

[tex]m<ABE=52\°[/tex]

substitute the values

[tex]2m<EBD+52\°=180\°[/tex]

[tex]2m<EBD=180\°-52\°[/tex]

[tex]m<EBD=128\°/2=64\°[/tex]

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

[tex]m<EBD+m<BED+m<EDB=180\°[/tex]

we have

[tex]m<EBD=64\°[/tex]

[tex]m<BED=90\°[/tex]

substitute

[tex]64\°+90\°+m<EDB=180\°[/tex]

[tex]m<EDB=180\°-(64\°+90\°)=26\°[/tex]

lublana

Answer:

B.[tex]26^{\circ}[/tex]

Step-by-step explanation:

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

[tex]\angleABE=52^{\circ}[/tex]

We have to find the measure of angle EDB.

Let [tex]\angle EBD=x[/tex]

Then, [tex]\angle CBD=x[/tex] because angle EBD is congruent to angle CBD.

[tex]\angle ABE+\angle EBD+\angle CBD=180^{\circ}[/tex] (linear sum)

[tex]52+x+x=180[/tex]

[tex]2x=180-52=128[/tex]

[tex]x=\frac{128}{2}=64^{\circ}[/tex]

In triangle EBD

[tex]\angle BED=90^{\circ}[/tex]

[tex]\angle EBD=64^{\circ][/tex]

[tex]\angle EBD+\angle BED+\angle EDB=180^{\circ}[/tex] (sum of angles of triangle )

Substitute the values then we get

[tex]64+90+\angle EDB=180[/tex]

[tex]154+\angle EDB=180[/tex]

[tex]\angle EDB=180-154=26^{\circ}[/tex]

Hence, [tex]m\angle EDB=26^{\circ}[/tex]

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