Measure of arc LN = ?

Given:

The figure of a circle.

To find:

The measure of LN.

Solution:

We know that the measure of arc is twice of measure of subtended angle on that arc.

In the given figure,

Substituting the value of angle from the given figure, we get

Therefore, the measure of arc LN is 94 degrees.

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

3 is greater then both of those numbers