Question

find the measure of ∠hkj.
diagram: lines ( fg ) (with points ( f, j, g )) and ( hi ) (with points ( h, k, i )) are parallel. transversal ( de ) (with points ( d, j, k, e )) intersects them. angle at ( j ) on ( fg ) is ( (15x - 1)^circ ), angle at ( k ) on ( hi ) is ( (6x - 8)^circ ).
( mangle hkj = square^circ )

Explanation:

Answer:

To find the measure of \( \angle HKJ \), we first recognize that lines \( FG \) and \( HI \) are parallel (since they are both horizontal and cut by a transversal \( DE \)). The angles \( (15x - 1)^\circ \) and \( (6x - 8)^\circ \) are same - side interior angles, and same - side interior angles are supplementary (their sum is \( 180^\circ \)).

So we set up the equation:
\[
(15x - 1)+(6x - 8)=180
\]
Combine like terms:
\[
15x+6x-1 - 8=180
\]
\[
21x-9 = 180
\]
Add 9 to both sides:
\[
21x=180 + 9=189
\]
Divide both sides by 21:
\[
x=\frac{189}{21}=9
\]

Now we find the measure of \( \angle HKJ \) by substituting \( x = 9 \) into the expression \( 6x-8 \):
\[
6(9)-8=54 - 8=46
\]

So \( m\angle HKJ=\boxed{46} \)