In DeltaJKL, bar(JL) is extended through point L to point M,m/_JKL=(3x+3)^(@), m/_LJK=(3x+17)^(@), and m/_KLM=(8x-16)^(@). Find m/_KLM. Answer:

Understand angles relationship: Understand the relationship between the angles in the problem. In any triangle, the sum of the interior angles is always 180 degrees. Additionally, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.Set up exterior angle equation: Set up the equation based on the exterior angle theorem. Since angle KLM is an exterior angle to triangle JKL, we have: m/_KLM = m/_JKL + m/_LJK Substitute the given expressions: (8x - 16) = (3x + 3) + (3x + 17)Simplify and solve for x: Simplify and solve for x. Combine like terms: 8x - 16 = 6x + 20 Subtract 6x from both sides: 2x - 16 = 20 Add 16 to both sides: 2x = 36 Divide by 2: x = 18Find angle KLM measure: Find the measure of angle KLM. Now that we have the value of x, we can substitute it back into the expression for m/_KLM: m/_KLM = 8x - 16 m/_KLM = 8(18) - 16 m/_KLM = 144 - 16 m/_KLM = 128 degrees

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In
DeltaJKL, bar(JL) is extended through point
L to point
M,m/_JKL=(3x+3)^(@),
m/_LJK=(3x+17)^(@), and
m/_KLM=(8x-16)^(@). Find
m/_KLM.
Answer:

In $\Delta \mathrm{JKL}, \overline{J L}$ is extended through point $\mathrm{L}$ to point $\mathrm{M}, \mathrm{m} \angle J K L=(3 x+3)^{\circ}$ , $\mathrm{m} \angle L J K=(3 x+17)^{\circ}$ , and $\mathrm{m} \angle K L M=(8 x-16)^{\circ}$ . Find $\mathrm{m} \angle K L M$ . $\newline$ Answer:

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Q. In

\Delta \mathrm{JKL}, \overline{J L}

is extended through point

\mathrm{L}

to point

\mathrm{M}, \mathrm{m} \angle J K L=(3 x+3)^{\circ}

\mathrm{m} \angle L J K=(3 x+17)^{\circ}

, and

\mathrm{m} \angle K L M=(8 x-16)^{\circ}

. Find

\mathrm{m} \angle K L M

\newline

Answer:

Understand angles relationship: Understand the relationship between the angles in the problem. $\newline$ In any triangle, the sum of the interior angles is always $180$ degrees. Additionally, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
Set up exterior angle equation: Set up the equation based on the exterior angle theorem. $\newline$ Since angle KLM is an exterior angle to triangle JKL, we have: $\newline$ $m/_{\text{KLM}} = m/_{\text{JKL}} + m/_{\text{LJK}}$ $\newline$ Substitute the given expressions: $\newline$ $(8x - 16) = (3x + 3) + (3x + 17)$
Simplify and solve for $x$ : Simplify and solve for $x$ . $\newline$ Combine like terms: $\newline$ $8x - 16 = 6x + 20$ $\newline$ Subtract $6x$ from both sides: $\newline$ $2x - 16 = 20$ $\newline$ Add $16$ to both sides: $\newline$ $2x = 36$ $\newline$ Divide by $2$ : $\newline$ $x = 18$
Find angle KLM measure: Find the measure of angle KLM. $\newline$ Now that we have the value of $x$ , we can substitute it back into the expression for $m/\_KLM$ : $\newline$ $m/\_KLM = 8x - 16$ $\newline$ $m/\_KLM = 8(18) - 16$ $\newline$ $m/\_KLM = 144 - 16$ $\newline$ $m/\_KLM = 128$ degrees