The other day， my brother drove his car down the street at ______ I thought was a dangerous speed.

C
显然后面是一个从句，throught后面的句子缺少主语，所以前面的空要填可以充当主语的词，所以排除A和B，而因为前面有一个at,所以不能加that，要加what.

what "那一天，我兄弟开着他的车以一个我认为危险的速度从街上驶过"

at 后面跟宾语，所以用what在这引导一个宾语从句，I thought 是个插入语，what在宾语从句中作主语相当于"a speed that".what相当于一一个名词+that。本句不能误当做定语从句而误选that或which。因为引导词前五先行词。

C. what
what I thought was a dangerous speed 是宾语从句，做介词at的宾语。

B which

C
what 引导的名词从句