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

Question

asked Nov 20, 2020 107k views

2 Answers

Mathias Stavrou · Answer 1 · 2020-11-25T16:31:28+0000

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
$O=3\cdot 35=105$