Question

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

Explanation:

Step1: Identify Angle Relationship

From the diagram (assuming \( \angle KNM \) and \( \angle MNJ \) are supplementary or form a linear pair, so \( m\angle KNM + m\angle MNJ = 180^\circ \)).
\[ 8x - 5 + 4x - 19 = 180 \]

Step2: Solve for \( x \)

Combine like terms:
\[ 12x - 24 = 180 \]
Add 24 to both sides:
\[ 12x = 180 + 24 = 204 \]
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:

\( 131^\circ \)