Question

I need help with both number 15 and 17 i don’t understand how to do it can you help?

Answer 1

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:

`\angle P+\angle Q=180^(\circ)`

Substitute the values given in the equation to get:

`\begin{gathered} 4x+1+9x-3=180 \\ 13x-2=180 \\ 13x=182 \\ x=14 \end{gathered}`

So the value of angle Q is:

`\angle Q=9x-3=9*14-3=123`

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:

`\begin{gathered} \angle J+\angle K=90 \\ \angle K-18+\angle K=90 \\ 2\angle K=108 \\ \angle K=54^(\circ) \end{gathered}`

Therefore the measure of the angle J is:

`\angle J=90-\angle K=90-54=36^(\circ)`

Hence J is 36 and K is 54 degrees.