Solve for the unknown angles. Justify your answers.

1. 31.67 degrees

2. 38 degrees

3.

PNQ  = 117 degrees

LKQ =  102 degrees

4. XYV = 120 degrees

Step-by-step explanation:

1. Using sum of angles of a triangle = 180

angle ACB = 180 - 55.14 - 93.19 = 31.67

2.

FDE = 180-GDE = 180 - 135.11 = 44.89   [angles on a line are supplementary]

FED = HEJ = 97.11         [vertical angles]

DFE = 180-FDE-FED = 180 - 44.89 - 97.11 = 38 degrees

3.

MLN = 180 - 82 = 98   [angles on a line are supplementary]

PNQ = 360 - 67 - 78 - 98 = 117  [sum of exterior angles of a polygon = 360]

LKQ = 180 - 78 = 102  [angles on a line are supplementary]

4.

WXY+YXZ = 180 [angles on a line are supplementary]

=>

3x + x = 180

=>

x = 180/4 = 45

Now solve for XYV

XYV = 360 - 135 - 60 - 45 = 120  [sum of interior angles of quadrilateral = 360]

Note: In the future, please limit the number of problems per question to three.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt