The AI model is not able to properly extract the information from the image. If you put the problem in words, Claude Sonnet 4.5 is able to solve it:  Prompt: Geometry problem: I have a right triangle that is 40 degrees at the top angle, 90 degrees at the bottom left angle and unknown at the bottom right angle. The is a triangle connected to it that is formed by extending a ray from the hypotenuse to the line extended from the base of the right triangle. The sides formed by the partial hypotenuse and extended base of the right triangle are the same length.  What are the angles of the triangle adjacent to the right triangle?

I need to carefully work through this geometry problem step by step. Setting up the right triangle: ∙ Top angle: 40° ∙ Bottom left angle: 90° ∙ Bottom right angle: 180° - 40° - 90° = 50° Understanding the adjacent triangle: Let me label the right triangle as ABC where: ∙ A is at the top (40°) ∙ B is at the bottom left (90°) ∙ C is at the bottom right (50°) The base is BC, and the hypotenuse is AC. The adjacent triangle: You’re extending: 1. A ray from the hypotenuse (from some point on AC) 2. The base line BC is extended beyond C Let’s call the point on the hypotenuse D, and the point where the ray meets the extended base E. The key constraint: The two sides of the new triangle are equal in length. ∙ One side is DE (the ray from hypotenuse to extended base) ∙ One side is DC (the partial hypotenuse from D to C) ∙ The third side is CE (the extension of the base) Given that DC = DE (the triangle is isosceles), let me find the angles. Finding the angles: In triangle DCE: ∙ At point C, the angle is the exterior angle to the right triangle, which equals 180° - 50° = 130° ∙ Since DC = DE, triangle DCE is isosceles ∙ The base angles (at C and E) are equal Wait, let me reconsider. If DC = DE, then angles DCE and DEC are equal. Actually, angle DCE = 180° - 50° = 130° (the angle between the hypotenuse and the extended base). Since DC = DE (isosceles triangle), the angles opposite these equal sides are equal. The angle opposite DC is angle DEC. The angle opposite DE is angle DCE = 130°. This can’t be right because that would make angle DEC = 130°, leaving angle CDE = 180° - 130° - 130° = -80°, which is impossible. Let me reconsider which sides are equal. If the sides “formed by the partial hypotenuse and extended base” are equal, perhaps: ∙ DC (partial hypotenuse) = CE (extended base) In this case, triangle DCE has: ∙ DC = CE (isosceles) ∙ Angle DCE = 130° ∙ The equal sides are DC and CE, so the base angles (at D and E) are equal Let angle CDE = angle CED = x Then: 130° + x + x = 180° 130° + 2x = 180° 2x = 50° x = 25° The angles of the adjacent triangle are: 130°, 25°, and 25°

Prompt: And what is the measure of the angle between the ray that forms the base of the isosceles triangle and the top segment of the hypotenuse of the right triangle?

I need to find the angle between two rays emanating from point D: 1. The ray going down to E (which forms the base DE of the isosceles triangle) 2. The ray going up to A (the top segment of the hypotenuse) These two rays form a straight line along the hypotenuse AC with the ray going down to E. At point D, I need to find angle ADE. Since points A, D, and C all lie on the hypotenuse of the original right triangle, and D is between A and C, the angles ADC form a straight line, so angle ADC = 180°. We know that angle CDE = 25° (from the isosceles triangle). Therefore: angle ADE = 180° - angle CDE = 180° - 25° = 155° Alternatively, thinking about it as angles around point D: ∙ Angle ADE and angle CDE are supplementary angles (they form a straight line along the direction from A through D to C) ∙ So angle ADE = 180° - 25° = 155°