# geometry

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Two angles <3 and <5 are supplementary to <4. If m<5 is 78 degrees, what is m<3? (A diagram is required, label the diagram)

• geometry -

I take this to mean that each of <3 and <5 is supplementary to <4. So,

m<3 + m<4 = 180
m<5 + m<4 = 180
In that case,
78 + m<4 = 180
m<4 = 102
Now, knowing that, w can find m<3:

m<4 + 102 = 180
m<4 = 72

This makes sense, since angles supplementary to a given angle are equal.

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