What is the main type of energy used to help convert metamorphic rocks into ingneous rocks in the rock cycle ?

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The main type of energy that is used to convert metamorphic rocks into igneous rocks is heat.

Metamorphic rock can only be converted into igneous rock by being melted and, thereby, made into magma.  The main type of energy that is used to melt a substance is, of course, heat.

If we were talking about changing igneous rocks into metamorphic rocks, then the answer would be different.  To do that, you need both heat and pressure.  But to melt metamorphic rocks into igneous rock, heat is what is needed.

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