Calculate the angle

Added: 2026-05-27

[00:00:00]Hi, my friends, and welcome to Math with Alex. Today, I have a beautiful geometry problem for you.

[00:00:07]Given is an isosceles triangle, and this triangle is divided into two smaller triangles.

[00:00:16]We know that one of the two smaller triangles is an isosceles triangle as well, and we know that this angle is equal to 75° and we are going to calculate this angle alpha.

[00:00:35]Okay, in the first step, we label the vertices of the triangles with A, B, C, and D.

[00:00:44]Triangle ABD is an isosceles triangle, and in an isosceles triangle, the base angles are equal.

[00:00:55]AB and BD have the same lengths, so the base angles are at A and D, and this means that the angle at D is equal to alpha as well.

[00:01:10]Triangle ACD is an isosceles triangle as well, because AD and DC have the same lengths.

[00:01:21]The base angles are at A and C, so this angle is equal to alpha as well.

[00:01:30]And now we can use the interior angle sum to calculate alpha.

[00:01:36]The three interior angles of a triangle always add up to 180°.

[00:01:42]So, in triangle ACD, is alpha plus alpha plus alpha plus 75° equal to 180°.

[00:01:56]Alpha plus alpha plus alpha is three times alpha, so we have three times alpha plus 75° is 180°.

[00:02:06]Now, we subtract 75° from both sides of this equation. This means that three times alpha is equal to 105°, and finally, we can divide both sides of this equation by three, so alpha is equal to 35°.

[00:02:26]Thanks for watching, my friends, and see you on the next video.