Determine the value of x.

Question

In the diagram, chords LM⎯⎯LM¯ and NP⎯⎯NP¯ are parallel and the measure of ∠M=68°. 

Determine the value of x. 

Answer 1

1. Since chords ML and PN are parallel, line MN is a transversal. Angles M and N are congruent and both equal 68° because they are alternate interior angles
2. Angles P subtends the same arc (LN) as angle M, so angle P is also 68º
3. The sum of the angles in the smaller triangle is:

m∠N + m∠P + x° = 180°

68° + 68° + x° = 180°

Solve for x°.