Chapter E, Problem 9.7EX

To determine

To find:The sum of the measures of $\angle ABC$ and $\angle ADC$ .

Answer to Problem 9.7EX

The sum of the measures of $\angle ABC$ and $\angle ADC$ is ${180}^{\circ }$ .

Explanation of Solution

Given information: Points A, B , and C lie on a circle in the order named $m\stackrel{⌢}{AB}=110$ and $m\stackrel{⌢}{BC}=120$ , point D lies on $\stackrel{⌢}{AC}$ .

Calculation:

Points A, B , and C lie on a circle in the order named $m\stackrel{⌢}{AB}=110$ and $m\stackrel{⌢}{BC}=120$

and point D lies on $\stackrel{⌢}{AC}$ .

Then points A, B , C and D become a cyclic quadrilateral.

  $\angle ABC+\angle ADC={180}^{\circ }$