Angle EMS = 180 degrees, MK-ray, divided this angle by a ratio of one to two Find the angle AMS

Angle EMS = 180 degrees, MK-ray, divided this angle by a ratio of one to two Find the angle AMS if MA is the bisector of EMK.

An angle of 180 ° is a straight line.

Since the MK divided the angle in a ratio of one to two, you can make up the following ratios of the angles:

EMK: KMS = 1: 2.

So, if we take the angle EMC for x, then the angle KMS = 2x. The sum of these two angles is 180. Find the angles EMC and KMS:

x + 2x = 180;

3x = 180;

x = 60о – angle EMC.

2x = 2 * 60 = 120о – KMS angle.

Since the MA beam is a bisector, it divides the EMC angle in half, which means that the AMK angle is equal to half of the EMC angle:

60: 2 = 30o – angle AMK.

Now, to find the AMS angle, you need to add the AMK angle to the KMS angle:

120 + 30 = 150o.

Answer: The AMS angle is 150 °.