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=(240^(\circ))/(16)`

`x=15^(\circ)`

Now, we will find the measure of angle RQS

`\angle RQS = 11x-65^(\circ)`

`\angle RQS = (11 * 15^(\circ))-65^(\circ)`

`\angle RQS = 100^(\circ)`