# Angles of a triangle with a tangent

• Nov 22nd 2011, 10:04 AM
Kyleee
Angles of a triangle with a tangent
Just before any of you say anything; Yes, I posted this a few days ago, but I didn't do the diagram correctly so I'll just post this new thread. :D

Okay, so :

I'm trying to work out the angles on the triangle and I'm having a little bit of difficulty. I tried working it but I'm not getting anywhere. Would the angle at the right of the 65 be 25? And would the one opposite to the "25" be "90"?
And by the way, the most important angle that I really need to get is the one at the tangent.

Diagram :
• Nov 22nd 2011, 11:40 AM
earboth
Re: Angles of a triangle with a tangent
Quote:

Originally Posted by Kyleee
Just before any of you say anything; Yes, I posted this a few days ago, but I didn't do the diagram correctly so I'll just post this new thread. :D

Okay, so :

I'm trying to work out the angles on the triangle and I'm having a little bit of difficulty. I tried working it but I'm not getting anywhere. Would the angle at the right of the 65 be 25? And would the one opposite to the "25" be "90"?
And by the way, the most important angle that I really need to get is the one at the tangent.

Diagram :

1. I've labeled the straight line segments and angles in your sketch. I assume that d is a diameter of the circle and that the upper left triangle is isosceles with x as equal legs (see attachment)

2. If my assumptions are correct then

• google for circle of Thales
• \$\displaystyle \angle(A)=65^\circ\$ Why?
• \$\displaystyle \angle(A) + \angle(B) = 180^\circ\$ Why?
• \$\displaystyle \angle(D) + \angle(B) + \angle(C)= 180^\circ\$ Why?
• \$\displaystyle \angle(D) + \angle(E) = 90^\circ\$ Why?
• Nov 22nd 2011, 07:28 PM
bjhopper
Re: Angles of a triangle with a tangent
Hi Kyleee,
You should state that the presumed diameter is perpendicular to the tangent at the point of tangency.
The figure can be erected in an infinite number of ways unless the point on the circle at the 65 deg inscribed angle has a defined arc from the top or bottom of the circle.
Wilmers assumption top arc= 90 deg
Earboths assumption top arc =80deg
bjh assumption top arc = 50 deg

If you do not know how to calculate angles for these cases google
chords and angles,complementry and supplemental angles, isosceles triangles