Question

QS bisects pqr. if mpqs = 5x and mrqs = 2x+6, then what is mpqr?

Answer 1

Okay, to start off, we 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)

$x = 6 ÷3$

x = 2

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

<PQR$= 2×10=20$

$<PQR= 20$ degree