Given: Angle OQR and angle RQS form a linear pair and measure of angle OQR = [tex] 5x+5^{\circ} [/tex] and measure of angle RQS= [tex] 11x-65^{\circ} [/tex]
To find: The measure of angle RQS.
Solution:
Since Angle OQR and RQS forms linear pair.
So, the sum of their angles is 180 degrees.
[tex] \angle OQR+\angle RQS=180^{\circ} [/tex]
[tex] 5x+5^{\circ}+11x-65^{\circ}=180^{\circ} [/tex]
[tex] 16x-60^{\circ}=180^{\circ} [/tex]
[tex] 16x=180^{\circ}+60^{\circ} [/tex]
[tex] 16x=240^{\circ} [/tex]
[tex] x=\frac{240^{\circ}}{16} [/tex]
[tex] x=15^{\circ} [/tex]
Now, we will find the measure of angle RQS
[tex] \angle RQS = 11x-65^{\circ} [/tex]
[tex] \angle RQS = (11 \times 15^{\circ})-65^{\circ} [/tex]
[tex] \angle RQS = 100^{\circ} [/tex]
