Hey Bro, I don't know if you still have issues with this but this is for anyone how is still experiencing this issue when trying to install DirectX.
I searched for hours and struggled to get this fixed, long story short I finally got it fixed!
Please try using the following link. Note: this is not a scam nor virus , it's from the official website (Microsoft)
Installing that fixed my issue.
1.Create an empty folder (The folder's name isn't important, just leave it blank for all I care)
2.Put the directx_Jun2010_redist.exe (That you just downloaded) into that empty folder.
3.Install/open the "directx_Jun2010_redist.exe"
4.Scroll through all the contents that were extracted, look for "DXSETUP.exe" and Install that.
5.Click through the on screen instructions and allow it to complete.
6.What are you still doing here you're DONE!! :)