QS bisects <PQR. m<PQS=5x and m<RQS = 2x+6, then what is m<PQR

Answer 1

Okay, to start off, you know that QS bisects <PQR, so that means the two angles created by that line, namely <PQS and <RQS, are equal. So let's do that:

5x = 2x+6

Now let's solve for x.

5x-2x = 2x-2x+6 (subtract 2x from both sides)

3x = 6 (simplify)

3x/3 = 6/3 (divide both sides by 3)

x = 2 (simplify)

Now that we've found the value of x, we can plug that back into either of the original equations. Both will output the same value: 10

The last step is to multiply it by 2 to get 20, which is the answer.