Just by filling in the angles, you can see that the remaining angle in each triangle must be 60°. To find ∠BCD, simply sum ∠BCA and ∠ACD to get a total of 60° + 90° = 150°.
Alternatively, you know that one of the longer sides is 350 meters, so the area can’t be larger than 350 × 350 = 122,500 square meters. The only answers that are less than this maximum value are (J) and (K). (K) is much too small to be a possible area, so you have found the correct answer, (J), with none of the algebra.
If you chose (K), you probably found the length of the shorter side and stopped there.
Since one side has a length of 9 millimeters, you know that the opposite side also has a length of 9 millimeters. To find the length of the bottom side (which will be the same as the top) sum all the line segments parallel to it: 5 + 2 + 1 + 3 = 11 millimeters. Therefore, the perimeter of the entire figure is 2(9) + 2(11) = 40 millimeters.
Since and are parallel lines intersected by two transversals, you know that the alternate interior angles are congruent. To find angle ∠DFG, look for its corresponding alternate interior angle, ∠ADF, given in the question as 50°.
Angles ∠BFE, ∠BFD, and ∠DFG all intersect at point F on a straight line, , so they are supplementary angles, meaning they add up to 180°. Inputting the expressions given for the two unknown angles, you can write out an equation solving for x:
If you got (C), you probably forgot to convert the leftover 0.28 hours to minutes, and left it as is.
You can eliminate (F), because ∠ABC and ∠BCD are alternate interior angles, formed by the transversal intersecting parallel lines and .
You can also eliminate (H), because ∠BDC and ∠BCD are opposite the two equal legs of an isosceles triangle so they are congruent as well.
If ∠BDC = ∠BCD, and ∠ABC = ∠BCD, then ∠BDC must also be equal to ∠ABC, eliminating answer choice (G).
Finally, you can eliminate (J), because ∠ACD and ∠CAB are both right angles formed by the line , which is perpendicular to the two parallel lines it crosses.
This leaves you with only one answer choice, (K). These two angle pairs are not congruent because, following from our above analysis, ∠ACB is 90° – ∠BDC. The two would only be equal if they were both 45°, and you cannot make that assumption.
If you chose (E), you probably left the height of the basketball net in inches.
If you picked (D), you probably divided the original height by 3 instead of multiplying.
Marking the diagram makes it clear that, if you subtract the length of from the sum of the two overlapping line segments, you get the overlap itself, : (32 + 26) – 50 = 58 – 50 = 8 units.
If you got (E), you probably thought the side length of the triangle was 64 units and misread the question.
If you chose (K), you probably forgot to square-root the value for x2.
If you chose (F), you found the perimeter of the smaller triangle.
Failing to remember your special triangles, you could draw out the pizza and solve for the diagonal using the Pythagorean Theorem:
If you chose (F), you aligned the 6” side of the box with the 32” side of the shelf, an orientation that can only fit boxes.
If you chose (H), you aligned the 6” side of the box with the 42” side of the shelf, a scenario that would fit only boxes.