Question

1. in △jkl, if m∠j is seven less than m∠l and m∠k is 21 less than twice m∠l, find the measure of each angle.

m∠j =
°
m∠k =
°
m∠l =
°

Explanation:

Step1: Define variables for angles

Let \( m\angle L = x \). Then \( m\angle J = x - 7 \) (since \( m\angle J \) is seven less than \( m\angle L \)) and \( m\angle K = 2x - 21 \) (since \( m\angle K \) is 21 less than twice \( m\angle L \)).

Step2: Use triangle angle sum theorem

The sum of the interior angles of a triangle is \( 180^\circ \). So, \( m\angle J + m\angle K + m\angle L = 180 \). Substituting the expressions for each angle:

$$ (x - 7) + (2x - 21) + x = 180 $$

Step3: Simplify and solve for \( x \)

Combine like terms:

$$ x - 7 + 2x - 21 + x = 180 \\ 4x - 28 = 180 $$

Add 28 to both sides:

$$ 4x = 180 + 28 \\ 4x = 208 $$

Divide both sides by 4:

$$ x = \frac{208}{4} \\ x = 52 $$

Step4: Find measures of each angle

• \( m\angle L = x = 52^\circ \)
• \( m\angle J = x - 7 = 52 - 7 = 45^\circ \)
• \( m\angle K = 2x - 21 = 2(52) - 21 = 104 - 21 = 83^\circ \)

Answer:

\( m\angle J = 45^\circ \)
\( m\angle K = 83^\circ \)
\( m\angle L = 52^\circ \)