What is the reason for statement 3 of the two-column proof? angle addition postulate definition of angle definition of complementary angles linear pair postulate given: the measure of angle j m k equals 52 degrees. the measure of angle k m l equals 38 degrees. prove: angle j m l is a right angle. art: three rays m l, m k, and m j share an endpoint m. ray m k forms a bisector. the bisector divides angle j m l into two parts labeled as j m k and k m l. statements reasons 1. m∠jmk=52°m∠jmk=52° given 2. m∠kml=38°m∠kml=38° given 3. m∠jmk+m∠kml=m∠jmlm∠jmk+m∠kml=m∠jml 4. 52°+38°=m∠jml52°+38°=m∠jml substitution property of equality 5. 90°=m∠jml90°=m∠jml simplification 6. ∠jml∠jml is a right angle. definition of right angle

Refer to the attached image.

Given:

The measure of and .

Also, Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.

To Prove: is a right angle.

Proof:

  Statements                                                                                 Reasons

1.                                            Given

2.                                           Given

3.  

The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.

4.   Substitution property of equality

5.                  Simplification

6. JML is a right angle.      Definition of right angle

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