1. AB has endpoints A(8,K) and B(7,3). The slope of AB is 5. What is K?
2. Two angles of a triangle measure 68 and 54. What is the measure of the third angle?
1. slope AB = (k-3)/(8-7) = 5
k-3 = 5
k = 8
2. let it be Ø
you know that Ø + 68 + 54 = 180
Ø = ....
G.58
1. Who needs a K when you have slope? Just kidding! Let's solve this math riddle. We know the slope of AB is 5. Using the formula (y2 - y1) / (x2 - x1), we can plug in the values for A and B: (3 - K) / (7 - 8) = 5. Simplifying, we get (3 - K) / -1 = 5. Multiplying both sides by -1, we find 3 - K = -5. Adding K to both sides, we get 3 = -5 + K. And finally, adding 5 to both sides, we get K = 8. So the mystery value is K = 8.
2. Ah, the enigmatic third angle of a triangle, always keeping us guessing! To find the measure of the third angle, we'll need to use some arithmetic comedy. We know that the sum of all three angles in a triangle is always 180 degrees. So, let's add up the given angles: 68 + 54 = 122. Now, subtract this sum from 180 degrees: 180 - 122 = 58. Voila! The measure of the third angle is 58 degrees. Triangle angles might not be great at telling jokes, but they definitely add up!
1. To find the value of K in the line AB, we can use the slope formula. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the two points given are A(8, K) and B(7, 3). The slope is given as 5. So, we can substitute the values into the formula:
5 = (3 - K) / (7 - 8)
Simplifying this equation gives us:
5 = (3 - K) / -1
To solve for K, let's cross-multiply:
5 * -1 = 3 - K
-5 = 3 - K
Now, isolate K by subtracting 3 from both sides of the equation:
-5 - 3 = -K
-8 = -K
Finally, to find the value of K, multiply both sides of the equation by -1:
8 = K
Therefore, the value of K is 8.
2. In a triangle, the sum of all three angles is always 180 degrees. To find the measure of the third angle, subtract the sum of the other two angles from 180.
Given that two angles of the triangle measure 68 and 54 degrees, the third angle can be found as follows:
Third angle = 180 - (68 + 54)
Simplifying the expression in parentheses:
Third angle = 180 - 122
Solving the subtraction:
Third angle = 58 degrees
Therefore, the measure of the third angle is 58 degrees.