Question

in △jkl, m∠j=(3x + 1)°, m∠k=(5x + 5)°, and m∠l=(4x + 6)°. find m∠l.

Explanation:

Step1: Use angle - sum property of triangle

The sum of interior angles of a triangle is $180^{\circ}$, so $(3x + 1)+(5x + 5)+(4x + 6)=180$.

Step2: Combine like - terms

$3x+5x + 4x+1 + 5+6=180$, which simplifies to $12x+12 = 180$.

Step3: Solve for $x$

Subtract 12 from both sides: $12x=180 - 12=168$. Then divide both sides by 12, so $x=\frac{168}{12}=14$.

Step4: Find $m\angle L$

Substitute $x = 14$ into the expression for $m\angle L$. $m\angle L=(4x + 6)^{\circ}=(4\times14 + 6)^{\circ}=(56+6)^{\circ}=62^{\circ}$.

Answer:

$62^{\circ}$