1. The problem asks to sketch an angle in standard position whose terminal arm passes through the point (1,5). 2. An angle in standard position has its vertex at the origin (0,0) and its initial side along the positive x-axis. 3. The terminal arm passes through the point (1,5), so we want to find the angle $\theta$ formed with the positive x-axis. 4. The angle $\theta$ can be found using the tangent function: $$\tan(\theta) = \frac{y}{x} = \frac{5}{1} = 5.$$ 5. To find $\theta$, take the arctangent (inverse tangent) of 5: $$\theta = \tan^{-1}(5).$$ 6. This angle is in the first quadrant since both $x$ and $y$ are positive. 7. The exact value of $\theta$ is $$\theta = \tan^{-1}(5)$$ which is approximately 78.69 degrees. 8. To sketch, draw the x-axis and y-axis, plot the point (1,5), and draw a ray from the origin through this point. The angle between this ray and the positive x-axis is $\theta$. Final answer: $$\theta = \tan^{-1}(5).$$