Question

Given: m∠PQR = x − 7, m∠SQR = x − 1, and m∠PQS = 100.
Find x.
The image is of three lines QR, QS and QP originating from a common point Q. QS is horizontal, QR is making acute angle with QS and QP is making obtuse angle with QS.
m∠POR + m∠SQR − m∠PQS a. _____
x − 7 + x − 1 = 100 b. Substitution Property
2x − 8 = 100 c. Simplify.
2x = 108 d. _____
x = 54 e. Division Property of Equality

Answer 1

So something like this I'm guessing

Answer 2

yes

Answer 3

can you help fill in the blank

Answer 4

when you wrote `m∠POR + m∠SQR − m∠PQS`

I'm assuming you meant to write this `m∠PQR + m∠SQR = m∠PQS`

Answer 5

the first line is Angle Addition Postulate

http://hotmath.com/hotmath_help/topics/angle-addition-postulate.html

it's the idea of gluing two angles together to form a bigger angle

Answer 6

what are your thoughts on the second blank?

Answer 7

I have no idea

Answer 8

what is happening to both sides when we go from `2x - 8 = 100` to `2x = 108`

are we subtracting something from both sides? adding? multiplying? or something else?

Answer 9

never mind its addition property of equality

Answer 10

yes, we add 8 to both sides