Answer:
AQ = 20 units
Step-by-step explanation:
Comparing triangle AQR to ABC,
=
=
cross multiply and make p the subject of formula, we have:
8p (2p+3) = 4p(6p-4)
16 + 24p = 24
- 16p
24p + 16p = 24 - 16
40p = 8
divide through by 8p,
p = 5
Therefore, AQ = 4p
= 4 × 5
= 20
AQ = 20 units
Answer:
Step-by-step explanation:
Answer: 66 degrees
Explanation:
Check out the attached image below. Figure 1 is the original image without any additions or alterations. Then in figure 2, I extend segment BC to form a line going infinitely in both directions. This line crosses segment DE at point F as shown in the second figure.
Note how angles ABC and DFC are alternate interior angles. Because AB is parallel to DE (given by the arrow markers) this means angle DFC is also 24 degrees
Focus on triangle DFC. This is a right triangle. The 90 degree angle is at C.
So we know that the acute angles x and 24 are complementary. They add to 90. Solve for x
x+24 = 90
x+24-24 = 90-24
x = 66
That is why angle CDE is 66 degrees
