Question

diagram shows points m, j, k, l, n with angles: ∠mj (132°), ∠jk (2x + 4)°, ∠ln (112°), forming a geometric figure (likely a triangle or polygon with exterior angles).

Explanation:

Step1: Find adjacent angles on straight lines

First, find the interior angles at \( J \) and \( L \) by using the linear pair (supplementary angles, sum to \( 180^\circ \)).
At \( J \): \( 180 - 132 = 48^\circ \)
At \( L \): \( 180 - 112 = 68^\circ \)

Step2: Use triangle angle sum property

The sum of angles in a triangle is \( 180^\circ \). Let the angle at \( K \) be \( (2x + 4)^\circ \). So:
\( 48 + 68 + (2x + 4) = 180 \)

Step3: Simplify and solve for \( x \)

Simplify the left - hand side:
\( 48+68 + 4+2x=180 \)
\( 120 + 2x = 180 \)
Subtract 120 from both sides:
\( 2x=180 - 120 \)
\( 2x = 60 \)
Divide both sides by 2:
\( x=\frac{60}{2}=30 \)

Answer:

\( x = 30 \)