To start the answer, Angular doesn't actually require jQuery. It has a built in version called
jQuery lite or jqLite-
jqLite is a tiny, API-compatible subset of jQuery that allows Angular
to manipulate the DOM in a cross-browser compatible way. jqLite
implements only the most commonly needed functionality with the goal
of having a very small footprint.
To return to the compatibility issues that form the thrust of your question.
Angular JS documentation specifically states that Internet Explorer 8 is not supported from version 1.3 onwards -
AngularJS 1.3 has dropped support for IE8. Read more about it on our
blog. AngularJS 1.2 will continue to support IE8, but the core team
does not plan to spend time addressing issues specific to IE8 or
earlier.
On the subject of Internet Explorer compatibility it also states-
The project currently supports and will attempt to fix bugs for IE9
and above. The continuous integration server runs all the tests
against IE9, IE10, and IE11...
We do not run tests on IE8 and below. A subset of the AngularJS
functionality may work on these browsers, but it is up to you to test
and decide whether it works for your particular app.
Source for both - Internet Explorer Compatibility, Angular JS Developer Guide
Given the substantial API and DOM changes between versions eight and nine of Internet Explorer - I'd not be surprised to find Angular 1.3 produces errors simply by being included in a page in Internet Explorer 8, although the abstractions provided with a version of jQuery from the 1.X branch may prevent issues provided that this is loaded before Angular JS (or at least before the DOMContentLoaded event is fired) thus ensuring it is used in place of the built-in jQuery lite provided with Angular JS. Given the DOM selector and event binding functions incorporated into jqLite this is presumably the most likely source of compatibility issues.
If your application needs to run in Internet Explorer 8 you would be wise to use the most recent legacy 1.2 version - 1.2.28 at the time of writing.
jQuery should be safe for your project providing you use the 1.x branch and not the streamlined 2.x branch, it has an excellent page on browser support should you wish to confirm this.
At the time of writing the 1.x branch maintains support back to Internet Explorer 6, and is unit tested against that browser. The 2.x branch features an identical API, but removes support for versions of Internet Explorer prior to 9 - to reduce the non-standard Internet Explorer API workarounds required for jQuery methods to work.
Looking forward to the 3.x releases, the split 1.x/2.y with identical APIs will be replaced by a single 3.x version number - and a separate "compatibility" branch/file will be simultaneously available for supporting a wider range of browsers. In the blog post announcing the release Internet Explorer 8 is specifically name-checked as being supported and with Internet Explorer 8 still enjoying between 3.43 and 5.49% based on current StatCounter data - you should still be safe using jQuery in your project for the foreseeable future.
Short answer
jQuery offers very different functionality to Angular JS and - although it is possible to rewrite an AngularJS app to only use jQuery, it will be much more verbose to achieve some behavior. I'm not going to go into the details of what makes Angular JS different from jQuery here, instead refer your to their Developer Guide Introduction.
The jQuery library enjoys much wider cited compatibility than AngularJS, but version 1.2 of AngularJS does still support Internet Explorer 8. If you want to use Angular then you should be able to safely do so using that version if Internet Explorer 8 is the earliest version you are required to support.
If you want the widest possible compatibility then you should use jQuery and not Angular JS for your application. With Internet Explorer 6 and 7 only enjoying 0.36% usage globally combined in Decemember 2014 though, Angular would seem a justifiable decision should you wish to use it.
As always, examine your target market/demographic for requirements before relying on global statistics.