AB and AC are equal legs in ABC. Point D lies on AB such that CD=CB. If ADC=114, what is ACD in degrees?

https://latex.artofproblemsolving.com/0/0/2/00269e96583c7f0dbf6e4cd0735f4b37ed1511f2.png

Saketh Sep 24, 2019

#1**0 **

If ADC = 114, then BDC = 180-114 = 66.

Since BC is congruent to DC, angle BDC is congruent to angle DBC, which is also 66 degrees

The angle measures of triangle BCD must add up to 180 degrees, so 66+66 = 132 and 180 - 132 = 48. So angle BCD = 48.

Now, side AB is congruent to side AC, so angle ABC is equal to angle ACB.

Can you solve it from there? (hint - angle ABC is also angle DBC.)

You are very welcome!

:P

CoolStuffYT Sep 24, 2019

#2**+1 **

Since CD = CB.....then angles DBC and BDC are equal

And since angle ADC = 116°.....then angle BDC = 180 - 116 = 64°

So angle DBC = 64°

Then angle DCB = 180 - 2(64) = 180 - 128 = 52°

And since AB = AC.....then angles ABC and ACB are equal

And angle ABC = angle DBC

So angle ACB = 64°

And angle ACB = angle DCB + angle ACD

So

64 = 52 + angle ACD subtract 52 from both sides

12° = angle ACD

a

CPhill Sep 25, 2019