j = 5 cm , k = 7 cm, and l = 10 cm
In the triangle shown, which shows the correct order of the angle measures from largest to smallest?
Note: Image is not drawn to scale.
Responses
A A, B, CA, B, C
B B, A, CB, A, C
C C, B, AC, B, A
D C, A, B
D) C, A, B
To determine the correct order of the angle measures in the triangle, we can use the fact that in a triangle, the sum of the angles is always 180 degrees.
Let's assume angle A, angle B, and angle C are the angles of the triangle.
Using the information given, we can set up the following equations:
angle A + angle B + angle C = 180 degrees
angle A + angle B + 10 degrees = 180 degrees (since l = 10 cm)
angle A + angle B = 170 degrees (equation 1)
angle B + angle C + 5 degrees = 180 degrees (since j = 5 cm)
angle B + angle C = 175 degrees (equation 2)
From equation 1 and equation 2, we can deduce that angle A must be smaller than angle C.
Now, let's compare angle A and angle B:
angle A + angle B = 170 degrees (equation 1)
angle B + angle C = 175 degrees (equation 2)
Since angle B is present in both equations, we can eliminate it by subtracting equation 1 from equation 2:
(angle B + angle C) - (angle A + angle B) = 175 degrees - 170 degrees
angle C - angle A = 5 degrees
From this equation, we can deduce that angle C must be larger than angle A.
Therefore, the correct order of the angle measures from largest to smallest is:
C, A, B
So, the correct answer would be D) C, A, B.