Chapter 5.3, Problem 1ACYP

To determine

To find: The measure less than $m\angle 1$ .

Answer to Problem 1ACYP

The measure of $m\angle 8$ $m\angle 3+m\angle 4$ and $m\angle 6+m\angle 5$ are less than $m\angle 1$ .

Explanation of Solution

Given:

The given figure is:

  

Calculation:

(Angle three plus angle four) and (angle six plus angle five) are the interior angle. Angle one is the corresponding exterior angle of the (Angle three plus angle four) and (angle six plus angle five).

Therefore by the exterior angle inequality theorem, the measure of angle $1$ is greater than $m\angle 3+m\angle 4$ and the measure of angle $1$ is greater than $m\angle 6+m\angle 5$ .