https://file.aiquickdraw.com/mathbot/file/1730388162012ks5h5opw.jpg

To solve for \( m \angle MLK \), let’s analyze the given triangle:

1. In the triangle \( \triangle MLK \), we see that:
   - Angle \( \angle M \) is given as \( 36^\circ \).
   - The marks on \( \overline{ML} \) and \( \overline{LK} \) indicate that these two sides are equal, meaning \( \triangle MLK \) is an **isosceles triangle**.

2. In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore:
   \[
   \angle MLK = \angle LKM
   \]

3. The sum of angles in any triangle is \( 180^\circ \). Therefore, we can write the equation:
   \[
   \angle M + \angle MLK + \angle LKM = 180^\circ
   \]

   Substituting \( \angle M = 36^\circ \) and knowing \( \angle MLK = \angle LKM \), we get:
   \[
   36^\circ + 2 \times \angle MLK = 180^\circ
   \]

4. Solving for \( \angle MLK \):
   \[
   2 \times \angle MLK = 180^\circ - 36^\circ
   \]
   \[
   2 \times \angle MLK = 144^\circ
   \]
   \[
   \angle MLK = \frac{144^\circ}{2} = 72^\circ
   \]

### Answer:
\[
m \angle MLK = 72^\circ
\]

Would you like a more detailed explanation, or do you have any questions?

Here are five related questions for further practice:
1. What is the measure of \( \angle LKM \) in \( \triangle MLK \)?
2. If \( \angle M \) was changed to \( 40^\circ \), what would \( m \angle MLK \) be?
3. Can you prove that the angles opposite equal sides in an isosceles triangle are always equal?
4. If \( \triangle MLK \) was equilateral, what would each angle measure?
5. How would the angle values change if \( \overline{ML} \) and \( \overline{MK} \) were unequal?

**Tip:** Remember, in any triangle, the sum of the interior angles is always \( 180^\circ \).

Find m∠MLK in the isosceles triangle ∆MLK where ∠M is 36°.

Learn how to find m∠MLK in the isosceles triangle ∆MLK where ∠M is given as 36°. This solution involves geometry concepts such as the sum of angles in a triangle and the Isosceles Triangle Theorem. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation