Geometry problem demonstrating the Angle Addition Postulate to find m∠KLM.

Problem:

The problem asks us to find the measure of angle \( \angle KLM \) given:
- \( m\angle KLB = 26^\circ \)
- \( m\angle BLM = 60^\circ \)

Solution:

#### Step 1: Understand the Angle Addition Postulate
The Angle Addition Postulate states that if a point lies in the interior of an angle, then the measure of the whole angle is the sum of the measures of the two smaller angles formed.

Mathematically, if point \( B \) lies in the interior of \( \angle KLM \), then:
\[
m\angle KLM = m\angle KLB + m\angle BLM
\]

#### Step 2: Identify the Given Information
From the problem, we are given:
- \( m\angle KLB = 26^\circ \)
- \( m\angle BLM = 60^\circ \)

Point \( B \) lies in the interior of \( \angle KLM \), so we can apply the Angle Addition Postulate.

#### Step 3: Apply the Angle Addition Postulate
Using the postulate:
\[
m\angle KLM = m\angle KLB + m\angle BLM
\]
Substitute the given values:
\[
m\angle KLM = 26^\circ + 60^\circ
\]

#### Step 4: Perform the Calculation
\[
m\angle KLM = 86^\circ
\]

#### Step 5: Write the Final Answer
The measure of \( \angle KLM \) is:
\[
\boxed{86^\circ}
\]

Explanation:

The Angle Addition Postulate is a fundamental principle in geometry that allows us to break down larger angles into smaller, more manageable parts. By adding the measures of the two smaller angles \( \angle KLB \) and \( \angle BLM \), we can determine the measure of the larger angle \( \angle KLM \). This method ensures accuracy and is a direct application of the postulate.

Thus, the final answer is:
\[
\boxed{86^\circ}
\]