Question

The measure of the angle between the internal and external bisectors of an angle is

• A. ${60}^{\circ }$
• B. ${70}^{\circ }$
• C. ${80}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is D ${90}^{\circ }$

In $\angle ABC$ , BD is the internal bisector

Then $\angle ABD=\angle DBC$ ,

In $\angle ABF$ ,BE is the external bisector

Then $\angle ABD=\angle DBC$ ,

The line FBC is strata line

Then $\angle ABD\angle DBC+\angle ABF+\angle EBF=180$

=$2(\angle ABD+\angle ABF)=180$

=$(\angle ABD+\angle ABF)={90}^0$

Then angle between the internal and external bisectors is ${90}^0$