Find the measure of angle 4 AND...… angle 7

<4 = 126

<7 = 55

Step-by-step explanation:

Remark

There are only 2 answers to this question. <4 has one of them and <7 has the other one. <7 is acute. <2 is obtuse.

Givens

<2 = 55 degrees

Solution

<4 is the supplement of <2

Therefore <4 + <2 = 180                     A straight line has an angle of 180°

<4 + 55 = 180

<4 = 180 - 55

<4 = 125

So <7 is either 55 or 125. Since <7 is acute, it is 55 degrees but we have another way of proving it.

<4 + <6 = 180 degrees            Interior angles on the same side of the transversal are supplementary

125 + <6 = 180

<6 = 180 - 125

<6 = 55

<7 =<6                                    Vertically opposite angles are equal.

<7 = 55 degrees.

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