Question

1. if ( mangle knm = (8x - 5)^circ ) and ( mangle mnj = (4x - 19)^circ ), find the measure of ( angle knm ).

Explanation:

Step1: Identify angle relationship

From the diagram, \( \angle KNM \) and \( \angle MNJ \) are supplementary (they form a linear pair), so \( m\angle KNM + m\angle MNJ = 180^\circ \).
Substitute the given expressions: \( (8x - 5) + (4x - 19) = 180 \).

Step2: Solve for \( x \)

Combine like terms: \( 8x + 4x - 5 - 19 = 180 \)
\( 12x - 24 = 180 \)
Add 24 to both sides: \( 12x = 180 + 24 \)
\( 12x = 204 \)
Divide by 12: \( x = \frac{204}{12} = 17 \).

Step3: Find \( m\angle KNM \)

Substitute \( x = 17 \) into \( 8x - 5 \):
\( 8(17) - 5 = 136 - 5 = 131 \).

Answer:

\( 131^\circ \)