Find the values of the angles shown in the diagram using rules of geometry

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The lines n and m are perpendicular (that is what the symbol between them means). This is to say that they are at right angles to each other.

The angles m1 and m2 are between n and m, and therefore are both right angles, ie 90 ` `degrees` `.

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The lines n and m are perpendicular (that is what the symbol between them means). This is to say that they are at right angles to each other.

The angles m1 and m2 are between n and m, and therefore are both right angles, ie 90 ` `degrees` `.

The angles m3 and m4 are adjacent angles on a straight line (line m) and so sum to 180 degrees or a half-turn. Since m3 = 54 degrees, then m4 = 180 - 54 = 126 degrees.

The angles m5 and m6 are opposite respectively to m3 and m4, and so are respectively equal or congruent to m3 and m4, so that m5 = 54 degrees and m6 = 126 degrees.

The angles m7 and m3 are Z angles, and so are equal or congruent, meaning that m7 = 54 degrees also.

Since lines n and l are perpendicular, then the angle between them m8 is a right angle, so that m8 = 90 degrees.

Angles m7 and m11 are complementary, that is, they sum to a right angles, so that m11 = 90 - m7 = 36 degrees.

Angles m9 and m11 are opposite each other, so that m9 = m11 = 36 degrees.

Angles m10 and m9 are adjacent on the line n and so sum to 180 degrees. Since m9 = 36 degrees, this implies that m10 = 180 - m9 = 144 degrees.

m1 = m2 = m8 = 90 degrees

m3 = m5 = m7 = 54 degrees

m4 = m6 = 126  degrees

m9 = m11 = 36 degrees

m10 = 144 degrees

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