Step-by-step explanation:
b is per the identity of angles on parallel lines when intersected by one inclined line the same as the 40° angle.
so,
b = 40°
due to the parallel nature of the 2 lines there is a symmetry effect for such shapes inscribed a circle. the upper and the lower triangle must be similar. and when applying a vertical line through the central crossing point, everything to the left is mirrored by everything on the right.
so, angle c must be equal to angle b.
c = 40°
and as the sum of all angles in a triangle is always 180°, d is then
d = 180 - 40 - 40 = 100°
the interior angle of the arc angle a is the supplementary angle of d (together they are 180°), because together with d they cover the full down side of the top-left to bottom-right line.
interior angle to a = 180 - 100 = 80°
due to the symmetry again, the arc angle opposite to a is the same as a.
as we know, the interior angle to a pair of opposing arc angles is the mean value of the 2 angles.
so, we have
(a + a)/2 = 80
2a/2 = 80
a = 80°
there might (and actually should) be some more direct approaches for "a" out of the other pieces of information, but that was the most straight one right out of my mind, and I don't spend time on finding additional shortcuts, when I have already a working approach.
Answer:
B
45 loaves x 5 cups/loaf = 225 cups
225 cups ÷ 4 cups/pound = 56.25 pounds
So basically you're dividing 12 by 3 times x which is 12 over 3x. 12/3x
The answer is 48 feet (D).
Explanation:
To solve this, you must think of the monument and its shadow and Adam and his shadow as a triangle, the person/object being the vertical leg, the shadows being the horizontal leg, and a line connecting them being the hypotenuse. Also, we can assume that these triangles are similar. First, we can set the scale to be 40/5 (the two shadows set a scale because the triangles are similar). Then, we can put x/6 (the actual things are similar, and the scale was established to be building/measurement). Next, we can set the two fractions equal to each other (40/5 = x/6) and solve. We can cross multiply to get 5x = 40 * 6. That goes to 5x = 240. Finally, we can divide by five on each side to get x = 48 feet (D).
