Question - Solving for x in a Geometry Problem with Exterior Angle Theorem
Solution:
This question involves a geometry problem with a triangle and an exterior angle. From the diagram, we see triangle ABC with an exterior angle DBC, which has a measure of (3x + 29)°. The interior angles opposite the exterior angle are angle BAC, which measures (6x + 14)°, and angle ABC, which appears to be a right angle (90°), as indicated by the little square box on angle ABC.According to the exterior angle theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles. Therefore, to solve for x, you would set up the equation based on the exterior angle theorem as follows:Exterior angle = Sum of opposite interior angles(3x + 29)° = (6x + 14)° + 90°Now let's solve for x.3x + 29 = 6x + 14 + 903x + 29 = 6x + 104Subtract 3x from both sides:29 = 3x + 104Subtract 104 from both sides:-75 = 3xDivide both sides by 3:-25 = xTherefore, x equals -25. However, if you are using this value of x to calculate angles in geometric problems, you should keep in mind that angle measures cannot be negative. There may be some information missing or a misunderstanding in interpreting the problem. Normally, you would expect to find a positive value for x in geometric problems involving angles. Please double-check to ensure there are no additional instructions or information provided that might affect the outcome of the solution.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com