# Genius Math

Triangle ABC has AC=BC, angle ACB=96 degrees. D is a point in ABC such that angle DAB=18 degrees and angleDBA=30 degrees. What is the measure in degrees of angle ACD?

I got 42 degrees!

1. 👍 0
2. 👎 0
3. 👁 743
1. Hmm, the triangle seems impossible, because if you draw it, given the condition that AC = BC (thus it's an isosceles triangle), then angle ACB = 96, therefore BAC = 96 degrees also (since the sides opposite to the angles are equal). So if there are two angles which are 96, the measure of the third angle ABC is
180 - 2(96)
= 180 - 192
= -12 degrees, which is impossible.
But well I'm not sure. I guess there is a typo or a figure given?

hope this helps :3

1. 👍 0
2. 👎 1
2. Since the original triangle is isosceles, it is easy to calculate that angle CAB =angle CBA = 42°
then angle CAD = 24° and angle CBD = 12°

then angle BDC = 360-x-132 = 258-x

in triangle ADC, by the sine law,
DC/sin24 = AC/sinx
DC = AC sin24/sinx

in triangle BCD,
DC/sin12 = BC/sin(22-x)
CD = BC sin12/sin(228-x)

ACsin24/sinx = BCsin12/sin(228-x)
but AC = BC, so let's divide both sides by AC

sin24/sinx = sin12/sin(228-x)
sin12(sinx) = sin24/(sin(228-x))
sin12 sinx = sin24/( (sin228cosx - cos228 sinx) )

sin12sinx = sin24sin228cosx - sin24cos228sinx
sinx(sin12 + sin24cos228) = sin24sin228cosx

sinx/cosx = sin24sin228/(sin12 + sin24cos228)
tanx = appr. 4.7046
x = 78°

then angle ACD = 180-78-24 = 78°

I have a feeling there is an easier way, but once your mind locks into a method of solution ......

1. 👍 0
2. 👎 0
3. I just notice two typos, but they don't affect the solution.

in the bracketed angle , it should say (228-x)

then angle BDC = 360-x-132 = 228-x

in triangle ADC, by the sine law,
DC/sin24 = AC/sinx
DC = AC sin24/sinx

in triangle BCD,
DC/sin12 = BC/sin(228-x)

1. 👍 0
2. 👎 0
4. it's 78

1. 👍 0
2. 👎 0
5. nju≈fgygkchfvfdc

1. 👍 0
2. 👎 0
6. 96°

1. 👍 0
2. 👎 0
7. 78°

1. 👍 1
2. 👎 0

## Similar Questions

1. ### Math

1. Name a pair of complementary angles. (1 point) 1 and 4 1 and 6 3 and 4 4 and 5 2. If m1=37°, what is m4? (1 point) 53° 43° 37° 27° 3. If m1 = 40°, what is m5? (1 point) 50° 40° 35° 25° Use the figure to answer

2. ### Math,geometry

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle ABP$, and $\angle ABC - \angle ACB = 39^\circ$. Find $\angle PBC$ in degrees.

3. ### maths-urgently needed

In right angled triangle ABC angle B=90 degree and AB= root 34 unit. The coordinates of point B and Care (4,2)and (-1,y) respectively. If area of triangle ABC = 17 sq.units, then find value of y.

4. ### Geometry

Problem: $AB$ and $AC$ are equal legs in $\triangle ABC$. Point $D$ lies on $AB$ such that $CD = CB$. If $\angle ADC = 114^\circ$, what is $\angle ACD$ in degrees?

1. ### geometry

1. Triangle ABC has a 63.0-degree angle at B, and side AC is 13.6 cm long. What is the diameter of the circle circumscribed about ABC? 2. And: Given any triangle ABC, with sides a, b, and c opposite angles A, B, and C,

2. ### Geometry

1. In an isosceles triangle that is not equilateral the angle between the congruent sides is called a ____ A> Leg B> Vertex C> Base D> Corollary

Point N is on hypotenuse BC of triangle ABC such than angle CAN is 45 degrees. If AC=8 and AB=6, find AN. I did Pythagorean Theorem for triangle ABC, and hypotenuse BC will be 10. I don't know how to continue from there. Oh, I'm

4. ### Precalculus

In most geometry courses, we learn that there's no such thing as "SSA Congruence". That is, if we have triangles ABC and DEF such that AB = DE, BC = EF, and angle A = angle D, then we cannot deduce that ABC and DEF are congruent.

1. ### Geometry 10

Triangle ABC is extended to point D Angle CAB =x+40 Angle ACB = 3x +10 angle CBD = 6x what is measure of angle CAB? I can get angles inside triangle to equal 180 but when I check for the extended point it does not add up to

2. ### MATHS

In triangle ABC, BC is produced to D. If angle ACD = 110 degree and angle ABC = 70 degree. Find angle BAC. Give reason.

3. ### math

Point X is on side of line AC of triangle ABC such that

4. ### Math

Which congruence statement says the same thing as triangle ABC is congruent to triangle DEF? (1 point) triangle ABC is congruent to triangle EFD triangle ACB is congruent to triangle DEF triangle ACB is congruent to triangle