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ElenaW [278]
3 years ago
5

What is the measurement of Angle O in parallelogram LMNO. When angle L is (x+40) and angle O is (3x)

Mathematics
2 answers:
Vlad1618 [11]3 years ago
8 0

Answer:

Angle <u>O(3x)</u> is =<em>105 degrees</em> or <em>C</em>

I am Lyosha [343]3 years ago
3 0

In a parallelogram, opposite angles are congruent.

This means that the four angles of the parallelogram are:

L = x+40,\quad M = 3x,\quad N = x+40,\quad O = 3x

Moreover, the sum of the interior angles of a polygon with n sides is 180(n-2). So, the sum of the interior angles of a parallelogram is 360.

This means

L+M+N+O = 360 \iff 2(x+40)+2(3x) = 2x+80+6x = 360 \iff 8x = 280 \iff x = 35

And since O=3x, we have O=3\cdot 35=105

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