Explain how two angles are equal

[Toranc3]

Homework Statement

Explain step by step how angle a is equal to angle a

Homework Equations

The sum of the angles in a triangle equal 180 degrees.

at a solution[/b]


[url=http://postimage.org/][PLAIN]http://s16.postimage.org/k0rslli05/untitled1.png[/url][/PLAIN]

Made two right triangles but I am not sure how to connect angle a from the big triangle to the small one. Not sure where to go from there. Thanks in advance!

 

[azizlwl]

Just extend those 2 arrows that meet the base, horizontal line.
First angle will be 90°
Let second angle be β

α+β=90°
β+x=90°

 

[Curious3141]

Homework Statement

Explain step by step how angle a is equal to angle a

Homework Equations

The sum of the angles in a triangle equal 180 degrees.

at a solution[/b][url=http://postimage.org/][PLAIN]http://s16.postimage.org/k0rslli05/untitled1.png[/url][/PLAIN]

Made two right triangles but I am not sure how to connect angle a from the big triangle to the small one. Not sure where to go from there. Thanks in advance!

I'm assuming this is not so much homework as you trying to understand what's in your book. So I'll give more direct help than what's usually allowed here.

See attached image. A, B refer to vertices of the big right triangle. a, b are vertices of the small triangle. C is common to both.

B is a right angle because a vertical line meets a horizontal line at B.

In the big triangle, angle ∠ACB = 180 - (α + 90) = 90 - α

angle ∠aCb = angle ∠ACB = 90 - α (opposite angles).

Finally, in the small triangle, ∠baC = 180 - (90 - α + 90) = α

You're done here, but for better understanding, you should be able to see that the big and small triangles (ABC and abC) are similar.

 

[LCKurtz]

And once you have done that, you will understand the theorem that two angles with mutually perpendicular sides sides are equal, just as two angles with mutually parallel sides are equal.