Chapter 1.5, Problem 5ST2

To determine

To complete: $m\angle 1+m\angle 2=m\angle \_\_\_$

Answer to Problem 5ST2

  $m\angle JOT$

Explanation of Solution

Given:

The figure:

Concept Used:

Angle addition postulate:

If point B lies in the interior of $\angle AOC$ , then

  $m\angle AOB+m\angle BOC=m\angle AOC$

From the Angle addition postulate, it can be said that,

  $m\angle JOK+m\angle KOT=m\angle JOT$ ….. (1)

Also, from the given figure, we have,

  $m\angle JOK=m\angle 1$

And

  $m\angle KOT=m\angle 2$

Substituting these values in equation (1),

  $m\angle 1+m\angle 2=m\angle JOT$