Question

If angke OQR and angke rqs form a linear pair and measure of anglr PQR = 5x+5 and measure of angle RQS= 11x-65 then measure of angle RQS= what

Answer 1

Given: Angle OQR and angle RQS form a linear pair and measure of angle OQR = $5x+5^{\circ}$ and measure of angle RQS= $11x-65^{\circ}$

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.

$\angle OQR+\angle RQS=180^{\circ}$

$5x+5^{\circ}+11x-65^{\circ}=180^{\circ}$

$16x-60^{\circ}=180^{\circ}$

$16x=180^{\circ}+60^{\circ}$

$16x=240^{\circ}$

$x=\frac{240^{\circ}}{16}$

$x=15^{\circ}$

Now, we will find the measure of angle RQS

$\angle RQS = 11x-65^{\circ}$

$\angle RQS = (11 \times 15^{\circ})-65^{\circ}$

$\angle RQS = 100^{\circ}$