Question

Triangle ABC has AB=AC and angle BAC =X, with X being less than 60 degrees. Point D lies on AB such that CB = CD Point E lies on AC such that CE= DE Determine angle DEC in terms of X

167

likes
833 views

Answer to a math question Triangle ABC has AB=AC and angle BAC =X, with X being less than 60 degrees. Point D lies on AB such that CB = CD Point E lies on AC such that CE= DE Determine angle DEC in terms of X

Expert avatar
Cristian
4.7
111 Answers
To determine angle DEC in terms of X, we need to first analyze the given information and then apply some geometric relationships.

Given: Triangle ABC with AB = AC and angle BAC = X.

Let's label the angles of triangle ABC as follows:

Angle BAC = X
Angle ABC = Y
Angle BCA = Z

We know that AB = AC, which means that angles ABC and ACB are also equal. Hence, ABC = ACB = Y.

Since angle BAC + angle ABC + angle BCA = 180 degrees (angle sum property of a triangle), we can write:

X + Y + Z = 180

Now, we need to determine the relationship between angle DEC and angle A. Since AB = AC, we have AD = AE. Furthermore, we know that CB = CD and CE = DE.

Using these equalities, we can conclude that triangles ACD and ADE are congruent by the Side-Angle-Side (SAS) congruence criterion.

Now, let's analyze triangle ACD. We know that the sum of angles in a triangle is 180 degrees. Therefore:

Angle ADC + angle CDA + angle CAD = 180

Since angle ADC = angle CDA (as triangles ACD and ADE are congruent), we can substitute them with x, resulting in:

x + x + (180 - 2x) = 180

Simplifying this equation, we get:

2x - 2x + 180 = 180

0 + 180 = 180

So, the equation is true, which means that our assumption is correct.

Therefore, angle DEC is equal to angle ACD, which is x.

Answer: Angle DEC = x (in terms of X)

Frequently asked questions (FAQs)
What is the average number of hours spent watching TV per week by a group of students?
+
Question: What is the derivative of y = sinh(x) + tanh(x) at x = π/4?
+
Question: What is the maximum value of the function f(x) = -2x^2 + 5x + 3 on the interval [-1, 3]?
+
New questions in Mathematics
calculate the derivative by the limit definition: f(x) = 6x^3 + 2
How many percent is one second out a 24 hour?
Find the equation of the normal to the curve y=x²+4x-3 at point(1,2)
Write 32/25 as a percent
58+861-87
If f(x) = 3x 2, what is the value of x so that f(x) = 11?
-3x 2y = -6; -5x 10y = 30
(-5/6)-(-5/4)
Solve this mathematical problem if 3/5 of a roll of tape measures 2m. How long is the complete roll?
If 0101, what is the binary representation of the 4x16 decoder output?
3.24 ÷ 82
Find the minimum value of the function y = -4 x3 + 60 x2 -252 x + 8 for values of x between x = 0 and x = 9 Enter the value of the function, not the value of x
If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable. 12, 18, 21, c, 13
a coffee shop has 9 types of creamer and 11 types of sweetener. In how any ways can a person make their coffee?
Today a father deposits $12,500 in a bank that pays 8% annual interest. Additionally, make annual contributions due of $2,000 annually for 3 years. The fund is for your son to receive an annuity and pay for his studies for 5 years. If the child starts college after 4 years, how much is the value of the annuity? solve how well it is for an exam
Find the symmetric point to a point P = (2,-7,10) with respect to a plane containing a point Po = (3, 2, 2) and perpendicular to a vector u = [1, -3, 2].
A grain silo has a height of 8.8m with a 11.4m diameter. If it is filled 0.5% of it's volume, how much grain (m^3) is stored in the silo? (0 decimal places)
Dano forgot his computer password. The password was four characters long. Dano remembered only three characters: 3, g, N. The last character was one of the numbers 3, 5, 7, 9. How many possible expansions are there for Dano's password?
Solve the system of equations by the addition method. 0.01x-0.08y=-0.1 0.2x+0.6y=0.2
Find the rule that connects the first number to the second number of each pair. Apply the rule to find the missing number in the third pair. (18 is to 22) (54 is to 26) (9 is to ?)