In a triangle, the measure of the first angle is three times the measure of the second angle. the measure of the third angle is 65 degrees more than the measure of the second angle. use the fact that the sum of the measures of the three angles of a triangle is 180 degrees to find the measure of each angle.

The three angles of the triangle are 69°, 23° and 88°

Explanation:

Assume that the measure of the second angle of the triangle is x

We are given that:

The measure of the first angle is three times the measure of the second one. This means that the first angle is 3x

The measure of the third angle is 65° more than the second angle. This means that the third angle is x + 65

Now, we know that the sum of the angles of a triangle is 180°

Therefore:

3x + x + x + 65 = 180

5x + 65 = 180

5x = 180 - 65

5x = 115

x = 23

Finally, we get the measures:

The first angle = 3x = 3(23) = 69°

The second angle = x = 23°

The third angle = x + 65 = 23 + 65 = 88°

Hope this helps :)

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.