+0

0
375
2
+128

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

Sep 24, 2019

#1
+1068
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

Sep 24, 2019
#2
+109334
+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

Sep 25, 2019
edited by CPhill  Sep 25, 2019