Find the measure of two supplementary angles if the diffrence in measure of the two angles is 24

The measure of two supplementary angles are

Solution:

Given that the difference of measure of the two angles is 24

Let the first angle be x and the second angle be x-24. We know when two angles are supplementary their sum is equal to

Now since x and (x-24) are two supplementary angles, therefore their sum will be equal to

x+(x-24) = 180

2x-24=180

2x= 180+24  

2x = 204

The first angle is

The second angle is (x – 24) so we get (102 - 24) = 78

Hence the measure of two supplementary angles are

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.