Ms. Garcia wants to estimate how much time students spend on homework, on average, during a typical week. She wants to estimate at the 90% confidence level with a margin of error of at most 30 minutes. A pilot study indicated that the standard deviation of time spent on homework per week is about 154 minutes. What’s the minimum number of students you would need to survey?

if triangle abc is congruent to triangle def, their interior angles are congruent, because congruent parts of congruent triangles are congruent (cpctc).

that means ∠d is congruent to ∠a; ∠d is equal to 8x - 2.

interior angles of all triangles add to equal 180 degrees, so you can set the sum of these interior angle values equal to 180 and solve for x.

180 = (8x - 2) + 22 + 72

180 = 8x - 2 + 22 + 72

180 = 8x + 92

88 = 8x

11 = x

x = 11