Question

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

Answer 1

Answer:

$O=180^o-\alpha$

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, $O+P=180^o$, or equivalently:

$O=180^o-P$

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

Angle $\alpha$ 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 $\alpha$.

$P=\alpha$

It follows that

$O=180^o-P=180^o-\alpha$

$\boxed{O=180^o-\alpha}$