Question

In the diagram below, angles JKL and LKM

are supplementary, mZJKL = (2x + 4)º,
and mZLKM = (x + 26)°. 7.6.5KM. What is mZJKL?
A.48°
B.50°
C. 104°
D. 116°

Answer 1

Given:

m∠JKL = (2x + 4)º

m∠LKM = (x + 26)º

Given that angles JKl and LKM are supplememtary, let's find the measure of angle JKL.

Supplementary angles are angles that sum up to 180 degrees.

Since both angles are supplementary, we have the equation:

m∠JKL + m∠LKM = 180

(2x + 4) + (x + 26) = 180

Let's solve for x.

Remove the parentheses:

2x + 4 + x + 26 = 180

Combine like terms:

2x + x + 4 + 26 = 180

3x + 30 = 180

Subtract 30 from both sides:

3x + 30 - 30 = 180 - 30

3x = 150

Divide both sides by 3:

`\begin{gathered} (3x)/(3)=(150)/(3) \\ \\ x=50 \end{gathered}`

To find m∠JKL, substitute 50 for x in (2x + 4):

m∠JKL = (2x + 4)°

m∠JKL = (2(50) + 4)°

m∠JKL = (100 + 4)°

m∠JKL = 104°

Therefore, the measure of angle JKL is 104 degrees

ANSWER:

C. 104°