Chapter 6.3, Problem 4ST1

To determine

Whether the given condition is true or false.

Answer to Problem 4ST1

The given condition is false.

Explanation of Solution

Given information :

It is given that in $\Delta ABC$ , $\angle BCD$ is an exterior angle, then $m\angle BCD>m\angle A+m\angle B$ .

Since, $\angle BCD$ is an exterior angle of $\Delta ABC$

From properties of triangle, that measure of exterior angle is equal to the measure of sum of two opposite interior angles.

Therefore,

  $m\angle BCD=m\angle A+m\angle B$

But we have given that $m\angle BCD>m\angle A+m\angle B$

Thus the given condition is false.