Solving for base angles in a congruent triangle

In summary, the conversation involved solving for base angles in a congruent triangle, where one base angle was given as 3x+5 and the other was unknown. The remaining angle was given as x+16. The conversation also mentioned using the sum of interior angles of a triangle (180 degrees) to solve for x. It was noted that setting 3x+5 equal to itself does not provide enough information to solve for x, and an additional equation is needed. Finally, the question of whether the triangle was congruent or isosceles was raised.
  • #1
tomtomtom1
160
8

Homework Statement



Solving for base angles in a congruent triangle
One of the base angles in a congruent triangle is 3x+5
The other base angle is unknown
The remaining angle is x+16.

Homework Equations



See attached PDF

The Attempt at a Solution



Because two base angles in a congruent triangle are the same and I have been given one of them I did the following:-

3x+5 = 3x+5 (I then tried to solve for x but this cancels out to 0.)

I want to know why this is the case, i think it is because i have 2 unknown variables but only1 equation.
 

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  • #2
tomtomtom1 said:

Homework Statement



Solving for base angles in a congruent triangle
One of the base angles in a congruent triangle is 3x+5
The other base angle is unknown
The remaining angle is x+16.

Homework Equations



See attached PDF

The Attempt at a Solution



Because two base angles in a congruent triangle are the same and I have been given one of them I did the following:-

3x+5 = 3x+5 (I then tried to solve for x but this cancels out to 0.)

I want to know why this is the case, i think it is because i have 2 unknown variables but only1 equation.

As you said, the other base angle is 3x+5. You need to use something else. What's the sum of all of the angles of a triangle?
 
  • #3
The sum of the interior angles of a triangle is 180Degrees.

But i want to know if making 3x+5 equal to itself 3x+5 (3x+5 = 3x+5) am i trying to solve for 1 unknown with 1 equation or am i trying to solve 2 unknowns with 1 equations?
 
  • #4
Setting 3x + 5 equal to itself implies 1 = 1. You need some other piece of information.
 
  • #5
tomtomtom1 said:
The sum of the interior angles of a triangle is 180Degrees.

But i want to know if making 3x+5 equal to itself 3x+5 (3x+5 = 3x+5) am i trying to solve for 1 unknown with 1 equation or am i trying to solve 2 unknowns with 1 equations?

As you said, the sum of your angles is 180 degrees. Write down an equation that expresses that.
 
  • #6
Also, why are you calling it a "congruent triangle"? Don't you mean "isoceles triangle"?

To expand on what others have said, what is the sum of the 3 angles in terms of x? Equate that expression to 180 degrees and solve.
 

Related to Solving for base angles in a congruent triangle

1. What is a congruent triangle?

A congruent triangle is a triangle that has the same size and shape as another triangle. This means that all three sides and all three angles of the triangle are equal.

2. Why is it important to solve for base angles in a congruent triangle?

Solving for base angles in a congruent triangle is important because it allows us to determine the measurements of all angles in the triangle. This is especially useful when working with geometric proofs and solving for unknown variables.

3. How do you solve for base angles in a congruent triangle?

To solve for base angles in a congruent triangle, we can use the fact that all three angles in a triangle add up to 180 degrees. So, if we know the measurement of one angle, we can subtract it from 180 and then divide the remaining sum by 2 to find the measurement of each of the base angles.

4. Can you use the Pythagorean Theorem to solve for base angles in a congruent triangle?

No, the Pythagorean Theorem only applies to right triangles and cannot be used to find the measurements of angles in a congruent triangle. However, it can be used to find the lengths of the sides in a congruent triangle.

5. Are there any other methods to solve for base angles in a congruent triangle?

Yes, there are other methods such as using trigonometric ratios or the Law of Sines and Law of Cosines. These methods are more advanced and typically used in more complex geometric problems.

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