。
Because she was angry, she stayed silent the whole time.
Literal
She [topic-は] angry was [because-ので] the-whole-time was-silent.
~ので provides a softer, more explanatory 'because' than ~から — fitting for a narrative account. ずっと黙っていた ('was silent the whole time') uses ずっと for duration and 黙る (to be silent) in its ~ていた (ongoing past state) form. The contrast between the intensity of 怒っていた and the quiet restraint of 黙っていた gives the sentence dramatic weight.