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

In ABC mBα Find the measure of the angle in degrees between the altitudes dropped from the vertices A and C class=

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elcharly64

Answer:

[tex]O=180^o-\alpha[/tex]

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, [tex]O+P=180^o[/tex], or equivalently:

[tex]O=180^o-P[/tex]

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

Angle [tex]\alpha[/tex] 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 [tex]\alpha[/tex].

[tex]P=\alpha[/tex]

It follows that

[tex]O=180^o-P=180^o-\alpha[/tex]

[tex]\boxed{O=180^o-\alpha}[/tex]

Ver imagen elcharly64

The measure of an angle is calculated by the property of supplement angle. Then the angle ∠O is 180 - α.

What is the triangle?

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

In ∆ABC, The angle ∠B = α.

In the right-angle triangle ∆ABE, angle ∠E is 90°, then we have

And we know that the ∠P and ∠O are supplement angles.

∠P + ∠O = 180

 α + ∠O = 180

       ∠O = 180 - α

More about the triangle link is given below.

https://brainly.com/question/25813512