Probability X is positive given X plus Y is positive

Let $X$ and $Y$ be independent standard normal variables. Compute the conditional probability that $X>0$ given that $X+Y>0$.

$3/4$. $(X,Y)$ is rotationally symmetric, so probabilities of wedges are proportional to their angles. The half-plane $X+Y>0$ spans $\pi$ radians, and the part of it with $X>0$ spans $3\pi/4$, giving $\tfrac34$.