In the figure above, ΔABC ≅ΔADE, ∠ACB = 105, ∠CAD = 10, and ∠B = 50. Find the measure of ∠DEF.

[potent tundra]

Tri ade is congruent to abc, so angle E = ACB and angle d = angle b

First find angle ead

[summer turret]

@potent tundra how would you do that if we don't know what <CAB is?

[potent tundra]

From triangle aed

@summer turret

Angle sum property

[summer turret]

Im not too sure what you mean because all angles of triangle AED is unknown no?

[potent tundra]

Triangle ade is congruent to abc

[summer turret]

oh <B = <E

[potent tundra]

So all the angles are equal

[summer turret]

and <ACB = <AED = 105

[potent tundra]

No E = C

[potent tundra]

Yeah

[summer turret]

so <EAD = 180-105-50=25

[potent tundra]

Same for angle B and angle D

[potent tundra]

Yeah

We have angle acb, find angle acf

[summer turret]

<ACF = 180-105=75

[potent tundra]

Yeah now find efa

[summer turret]

but angle AEF is not known how?

[potent tundra]

Ok find afc

[summer turret]

how would you do that?

[potent tundra]

This and we have angle cad

Angle sum property

[summer turret]

oh right <CAD

so <ACF = 180-75-10 = 95

[potent tundra]

Yeah

Do you know abt vertically opp angles

[summer turret]

yes

so <EFD = 95

[potent tundra]

Yes so now find efd

[potent tundra]

Yeah

We have angle D and efd

Now angle sum property

For def

[violet oracle]

Gawd daym

[summer turret]

<DEF = 180-95-50=35

alr thanks

[potent tundra]

Yep

[summer turret]

can you help me with another one?

[potent tundra]

If I can, sure

[summer turret]

I will add you

[potent tundra]

Just send it here