1. What is the area of the rectangle whose coordinates are (-6,-1) (-3,-4) (-1,-2) and (-4,1)?

2. What is the value of x?

[180  − 52 ] / 2  = 64“  = a base angle of the triangle on the left

180 − 64  = 116°   supplemental  angle to this base angle

[180 − 116] / 2  =  x  =  32°

3.   [9x + 2]  = [2x + 4] + [6x + 6 ]     [exterior angle theorem]

9x + 2  = 8x + 10 

x = 8

So.....m < PQS  = 9(8) + 2  = 74°

P. S.  ...   I'll solve the first one in a bit

1. Distance beween (−4,1) and (−1,−2)  = √ [( −4 − −1)^2  + ( −2 − 1)^2 ]  = √[ 9 + 9] = 3√2

    Distance beween (−4,1) and (−6,−1)  = √ [( −4 − −6)^2  + ( −1 − 1)^2 ]  = √[ 4 + 4] = 2√2

Area =  3√2 * 2√2  =  6√4  = 6 * 2  = 12  units^2 

Thank you!