Question

find the degree measure of each angle in the triangle.
$mangle k = square^circ$
$mangle l = square^circ$
$mangle m = square^circ$

Explanation:

Step1: Identify triangle type

The triangle has a right angle at \( K \), so it's a right triangle. The sum of angles in a triangle is \( 180^\circ \), and the right angle \( \angle K = 90^\circ \). So the sum of \( \angle L \) and \( \angle M \) is \( 180 - 90 = 90^\circ \).

Step2: Set up equation for \( \angle L \) and \( \angle M \)

Given \( \angle L=(3x + 42)^\circ \) and \( \angle M=(5x + 8)^\circ \), we have:
\( (3x + 42)+(5x + 8)=90 \)
Simplify: \( 8x + 50 = 90 \)

Step3: Solve for \( x \)

Subtract 50 from both sides: \( 8x = 90 - 50 = 40 \)
Divide by 8: \( x=\frac{40}{8}=5 \)

Step4: Find \( \angle L \) and \( \angle M \)

For \( \angle L \): \( 3x + 42 = 3(5)+42 = 15 + 42 = 57^\circ \)
For \( \angle M \): \( 5x + 8 = 5(5)+8 = 25 + 8 = 33^\circ \)

Answer:

\( m\angle K = 90^\circ \)
\( m\angle L = 57^\circ \)
\( m\angle M = 33^\circ \)