2 years ago

In the given circle the m∠DFB is 41°, mArc EF is 52° what is the m∠C ?

1 answer:

Naily [24]2 years ago

4 0

Check the picture below.

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I am Lyosha [343]

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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hammer [34]

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