Question

1. find the measure of each angle.

m∠ljk=

m∠mlk=

(handwritten equations: 15y - 2 = 4y + 8 + 8y + 11; 15y - 2 = 12y + 19)

Explanation:

Step1: Use Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(15y - 2=(4y + 8)+(8y+11)\)
Simplify the right - hand side: \(4y + 8+8y + 11=12y+19\)
So the equation becomes \(15y-2 = 12y + 19\)

Step2: Solve for y

Subtract \(12y\) from both sides: \(15y-12y-2=12y - 12y+19\)
\(3y-2 = 19\)
Add 2 to both sides: \(3y-2 + 2=19 + 2\)
\(3y=21\)
Divide both sides by 3: \(y=\frac{21}{3}=7\)

Step3: Find \(m\angle LJK\)

Substitute \(y = 7\) into the expression for \(\angle LJK\): \(m\angle LJK=4y + 8\)
\(m\angle LJK=4\times7+8=28 + 8=36^{\circ}\)

Step4: Find \(m\angle MLK\)

Substitute \(y = 7\) into the expression for \(\angle MLK\): \(m\angle MLK=15y-2\)
\(m\angle MLK=15\times7-2=105 - 2=103^{\circ}\)

Answer:

\(m\angle LJK = 36^{\circ}\), \(m\angle MLK=103^{\circ}\)