In angle JKL, KL congruent JL, M angleK + 2x-36 and m angleL+x+2 find M angle J

You are dealing with an isosceles triangle \( \triangle JKL \), where \( KL \cong JL \). This means that angles opposite the congruent sides, \( \angle J \) and \( \angle L \), are also equal.

Here is the breakdown:

1. Since \( KL \cong JL \), we have \( m \angle J = m \angle L \).
2. The angle measures are given as:
   - \( m \angle K = 2x - 36 \)
   - \( m \angle L = x + 2 \)

Since the sum of all angles in a triangle is always \( 180^\circ \), we can set up the following equation:

\[
m \angle J + m \angle K + m \angle L = 180^\circ
\]

Since \( m \angle J = m \angle L \), we can substitute \( m \angle J \) with \( x + 2 \):

\[
(x + 2) + (2x - 36) + (x + 2) = 180
\]

Now, let's solve for \( x \).

\[
2x + 4 + 2x - 36 = 180
\]
\[
4x - 32 = 180
\]
\[
4x = 212
\]
\[
x = 53
\]

Now that we know \( x = 53 \), we can find the measures of the angles.

1. \( m \angle L = x + 2 = 53 + 2 = 55^\circ \)
2. \( m \angle J = m \angle L = 55^\circ \)
3. \( m \angle K = 2x - 36 = 2(53) - 36 = 106 - 36 = 70^\circ \)

Thus, \( m \angle J = 55^\circ \).

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you determine congruent angles in isosceles triangles?
2. What is the sum of the interior angles of any triangle?
3. How would the problem change if \( KL \) was not congruent to \( JL \)?
4. What is the relationship between the angles of an equilateral triangle?
5. How do you verify your solution by checking the sum of all angles?

**Tip:** Always double-check that the sum of the angles in a triangle equals 180°.

In angle JKL, KL congruent JL, M angle K + 2x - 36 and M angle L + x + 2, find M angle J.

This problem helps students solve for an unknown angle in an isosceles triangle, applying algebraic methods. Learn how to find angle J when KL is congruent to JL, using key theorems like the Angle Sum Theorem and the Isosceles Triangle Theorem. Suitable for Grades 8-10.

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