Question

choose the correct angle addition formula for the diagram below.

a ( mangle lkm + mangle mkn = mangle lkn )
b ( mangle lkm + mangle lkn = mangle mkn )
c ( mangle mkn + mangle lkn = mangle lkm )
d ( mangle mlk + mangle mnk = mangle nlk )

(diagram: point ( k ) with rays ( kl ), ( kw ), ( kn ); angle between ( kl ) and ( kw ) is ( (2x + 10)^circ ), between ( kw ) and ( kn ) is ( (4x - 3)^circ ).)

Explanation:

Step1: Analyze the Angle Addition Postulate

The angle addition postulate states that if a point lies in the interior of an angle, the sum of the two smaller angles formed is equal to the measure of the larger angle. Looking at the diagram, angle \( \angle LKN \) is composed of \( \angle LKM \) and \( \angle MKN \). So, by the angle addition postulate, \( m\angle LKM + m\angle MKN = m\angle LKN \).

Step2: Evaluate the Options

• Option A: Matches the angle addition postulate as explained.
• Option B: Incorrectly sums \( \angle LKM \) and \( \angle LKN \) to get \( \angle MKN \), which is the reverse of the correct relationship.
• Option C: Incorrectly sums \( \angle MKN \) and \( \angle LKN \) to get \( \angle LKM \), which is not consistent with the angle addition postulate.
• Option D: Involves angles \( \angle MLK \), \( \angle MNK \), and \( \angle NLK \) which are not related in the diagram as per the angle addition postulate for the given angle \( \angle LKN \).

Answer:

A. \( m\angle LKM + m\angle MKN = m\angle LKN \)