I want to round out this right angle join between two edges. How can I achieve this effect in red?

enter image description here

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    $\begingroup$ One thing you can try is to use the bevel command Ctrl+Shift+B on that vertex. It probably won't exactly lead you to the desired effect but it brings you closer to where you want to go. Once you've beveled the vertex you can use the loop cut tool Ctrl+R on the edge to add some cuts. After that you would have to move the vertices manually to the desired position. $\endgroup$ – Pandatology Nov 24 '17 at 15:13

There may be many ways to do it (using the knife project or to sphere tools e.g.). I'll show you a method wich uses a spin tool though. enter image description here

Select the vertex which creates the straight angle and rip it (V). After selecting two vertices press G twice to slide them. This way you can set the size of the round joint. enter image description here

Next with the two vertices selected snap the cursor to them (Shift+S-->Cursor to Selected). Change the pivot point type to 3D Cursor and enable snapping tool (Vertex). Select the bottom vertex, snap the cursor to it and (being in side view) press the Spin button (set the steps number in a Tool Shelf as you like). Next select the vertices of the arc, rotate and scale it to make the joint. enter image description here

Finally remove doubles (select the whole mesh with A, then press W-->Remove Doubles). Fill the hole with F. enter image description here

UPDATE: Using to sphere tool: enter image description here

Select the vertex which creates the straight angle, press Shift+Ctrl+B and set the arc's size. Enable snapping tool (Vertex). Extrude the bottom vertex and snap it to the other one as pictured below. Snap the cursor to it (with 3D Cursor pivot point type), then delete it. Select the diagonal edge, subdivide it (W-->Subdivide) and set the subdivisions number in a Tool Shelf. Next press Shift+Alt+S,1. Finally translate the arc along Y and Z axes to snap it to the other vertices. enter image description here

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