Question

make connections solve the problem. in triangle jkl, m∠k is four times m∠j, and m∠l is five times m∠j. what is the measure of each angle? m∠j = °, m∠k = °, m∠l = °

Explanation:

Step1: Define variables for angles

Let \( m\angle J = x \). Then \( m\angle K = 4x \) (since it's four times \( m\angle J \)) and \( m\angle L = 5x \) (since it's five times \( m\angle J \)).

Step2: Use triangle angle sum property

The sum of angles in a triangle is \( 180^\circ \). So, \( x + 4x + 5x = 180^\circ \).

Step3: Solve the equation

Combine like terms: \( 10x = 180^\circ \). Then, divide both sides by 10: \( x=\frac{180^\circ}{10}=18^\circ \).

Step4: Find measures of other angles

\( m\angle K = 4x = 4\times18^\circ = 72^\circ \).
\( m\angle L = 5x = 5\times18^\circ = 90^\circ \).

Answer:

\( m\angle J = 18^\circ \), \( m\angle K = 72^\circ \), \( m\angle L = 90^\circ \)