The angles opposite the congruent sides of an isosceles triangle are congruent. Find the value of x in the triangle. Show all your work.

Question

The figure shows a triangle with 2 congruent sides. The angle between the congruent sides measures x degrees and a different angle measures 70 degrees.

Answer 1

Let's call the other angle opposite the congruent side "y".

We know that the sum of the interior angles in a triangle is 180 degrees, so we can set up an equation:

x + y + 70 = 180

We also know that the angles opposite the congruent sides are congruent, so:

x = y

We can substitute y for x in the equation:

y + y + 70 = 180

2y + 70 = 180

Subtract 70 from both sides:

2y = 110

Divide by 2:

y = 55

Since x and y are congruent angles, x must also be 55 degrees.

Therefore, the value of x in the triangle is 55 degrees.

Answer 2

make it shorter so i can put it in my words

Answer 3

1. Let's call the other angle opposite the congruent side "y".
2. We know that x + y + 70 = 180.
3. Since x and y are congruent, we can substitute y for x in the equation.
4. Solving for y, we get y = 55.
5. Therefore, x must also be 55 degrees.
6. The value of x in the triangle is 55 degrees.