Answer :
15. It is given that P and Q are supplementary which means that the sum of both the angles is 180 degrees so it follows:
[tex]\angle P+\angle Q=180^{\circ}[/tex]Substitute the values given in the equation to get:
[tex]\begin{gathered} 4x+1+9x-3=180 \\ 13x-2=180 \\ 13x=182 \\ x=14 \end{gathered}[/tex]So the value of angle Q is:
[tex]\angle Q=9x-3=9\times14-3=123[/tex]Hence angle Q is 123 degrees.
17. It is given that J and K are complementary angles that means the sum is 90 degrees. It is also given that angle J is 18 less than K so it follows:
[tex]\begin{gathered} \angle J+\angle K=90 \\ \angle K-18+\angle K=90 \\ 2\angle K=108 \\ \angle K=54^{\circ} \end{gathered}[/tex]Therefore the measure of the angle J is:
[tex]\angle J=90-\angle K=90-54=36^{\circ}[/tex]Hence J is 36 and K is 54 degrees.