Geometry Homework Help Pleasee!!?

Question

Please help me with these two problems and if you can, can you tell or show me how to do it step-by-step?

QS bisects angle PQR, angle PQR = x squared, and angle PQS = (2x+ 6 ). Find all the possible measures for angle PQR.

The answer is 36 and 4 but I'm the type of person that wants to learn how to get this answer...

and the second question is...

Angle ABC is congruent to angle DBC. Angle ABC = (3x/2 + 4) and and DBC = ( 2x- 27 1/4 ). Is angle ABD a straight angle? Explain.

Answer 1

On the first, 2x + 6 would equal half of x^2 since that's what bisect means.  So if you double it you should bet x^2.

x^2 = 4x + 12  Now make it equal zero

x^2 - 4x - 12 = 0 and factor it

(x - 6)(x + 2) = 0

so x = 6 or -2

making x^2 be 36 or 4

On the next you have (3x/2 + 4) = (2x - 27 1/4)

Change to decimals: 1.5 x + 4 = 2x - 27.25

add -1,5x to both sides and add 27.25 to both

31.25 = 0.5x

divide both by 0.5 getting x = 62.5

Plug that in for x; if each comes out 90 then it's a straight angle