Math assignment!!!

1.) Angle X and Angle Y are supplementary. Find the measure of each angle if Angle Measurement X= 6x -1 and Angle MEasurement Y=5x -17.

Two angles that sum to a straight angle $180^{\circ}$are called supplementary angles.

$\begin{array}{rcl} X &=& 6x-1 \\ Y &=& 5x-17 \\ X+Y &=& 180^{\circ} = 6x-1 + 5x-17\\ 180^{\circ} &=& 11x-18\\ 180^{\circ}+18 &=& 11x\\ 198 &=& 11x\\ 11x &=& 198 \\ x &=& \frac{198}{11} \\ x &=& 18 \\\\ X &=& 6x -1\\ X &=& 6\cdot 18 -1 \\ X &=& 107^{\circ}\\\\ Y &=& 180^{\circ} -X \\ Y &=& 180^{\circ} -107^{\circ}\\ Y &=& 73^{\circ} \end{array}$

2.) /P and /Q are complementary. The measure of /Q is 4 times the measure of /P. Find the measure of each angle.

Complementary angles are angle pairs whose measures sum to one right angle $90^{\circ}.$

$\begin{array}{rcl} Q &=& 4P\\ P + Q &=& 90^{\circ}\\ P + 4P &=& 90^{\circ}\\ 5P &=& 90^{\circ}\\ P &=& \frac{ 90^{\circ} }{5}\\ P &=& 18^{\circ}\\\\ Q &=& 90^{\circ} - P \\ Q &=& 90^{\circ} - 18^{\circ}\\ Q &=& 72^{\circ}\\ \end{array}$