In ∆ABC, m∠B=α. Find the measure of the angle, in degrees, between the altitudes dropped from the vertices A and C.

Step-by-step explanation:

Relations Between Angles

We need to recall some properties of the angles to find the angle marked as O.  Please refer to the image attached.

First, if two angles O and P are formed from the intersection of a line with a secant line, their sum is 180°.

From the figure, , or equivalently:

Second, if an angle is formed by the intersection of two lines, then the same angle will be formed by the intersection of two lines perpendicular to the original lines.

Angle is formed by the intersection of BC and BA. The segment EA is perpendicular to BC and CD is perpendicular to BA, thus the angle P is congruent to the angle .

It follows that

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10