Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°
<u>Step-by-step explanation:</u>
Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL
KM ≅ LM
3x + 23 = 7x - 37
23 = 4x - 37
60 = 4x
15 = x
KM = LM = 3x + 23
= 3(15) + 23
= 45 + 23
= 68
KL = 9x - 40
= 9(15) - 40
= 135 - 40
= 95
Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.
- Since N is the midpoint of KL and KL = 95, then NL = 47.5
- Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse
Use trig to solve for ∠L (which equals ∠K):
cos ∠L = 
cos ∠L = 
∠L = cos⁻¹ 
∠L = 45.7
Triangle sum Theorem:
∠K + ∠L + ∠M = 180°
45.7 + 45.7 + ∠M = 180
91.4 + ∠M = 180
∠M = 88.6
Answer:
16.67% increase
Step-by-step explanation:
finding the percentage price increase
we need to find the difference in percentage price between the 2 years
12%-10% = 2%
2%/12% x 100% = 100%/6 = 16.67%
20% increase between January 1st 2010 and January 1st 2011
Answer:
4, 10
Step-by-step explanation:
The value for the third side of the triangle is given by
b-a < n < b+a where a and b are the two other sides of the triangle and b>a
7-4 < n < 7+4
3 < n < 11
Since n is an integer
4 would be the smallest value and 10 would be the largest
Complementary angles are angles who sum to 90 degrees. So, since one angle is 13 degrees, naturally the other must equal 77. Good luck! c: