Angle Bisector of Triangle

The external bisectors of $\angle B$ and $\angle C$ of $∆\mathrm{ABC}$ meet at point $P$. If $\angle BAC=80°$, then find the $\angle BPC$.

$ABC$ is an isosceles triangle such that $AB=AC$ and $\angle B=35°$, $AD$ is the median to base $BC$ then $\angle BAD$ is:

In $∆ABC$, $AD$ is the bisector of $\angle BAC$. If $BD = 2 \mathrm{cm}$, $CD = 3 \mathrm{cm}$ and $AB = 5 \mathrm{cm}$. Find the length $AC$.

If angle bisector of a triangle bisect the opposite side, then what type of triangle is?

The triangle $PQR$ is right-angled at $R.$ If $PQ=8.5 cm, QR=8.4 cm \& PR=k cm$, then find the value of $k.$

In triangle $ABC:$ $\angle A=60°, \angle C=40°$ and bisector of angle $ABC$ meet side $AC$ at the point $P.$ Check whether $BP=CP.$

In the given figure, $∆ABC$ is triangle such that $\frac{AB}{AC}=\frac{BD}{DC}, \angle B=70°, \angle C=50°.$ If the $\angle BAD=k°$ then find the value of $k.$ 

In a $∆ABC,$ if point $D$ is on the $BC$ such that $\frac{AB}{AC}=\frac{BD}{DC}$ and $\angle B=70°, \angle C=50°$. If the $\angle BAD=k°$ then find the value of $k$.

In a $∆XYZ,$ if the internal bisector of $\angle X$ meets $YZ$ at $\text{'}P\text{'},$ then which of the following is true.

If $BD$ is the perpendicular bisector of $AC$. Find the value of $x$.

If $BD$ is the perpendicular bisector of $AC$. Find the value of $x$. 

In the figure, $XY$ is the bisector of $\angle ZXW$. $\angle ZXY=75°$, $\angle PXW$ is _____$°$

In the figure, $OB$ is the bisector of $\angle AOC$. Find $\angle AOB$(in degrees)

If $I$ is the in-centre of the triangle $ABC$ then find the value of $x$ in the figure

Prove that if $I$ is the in-centre of the triangle then line segments $AE \text{and} AG, CG \text{and} CF, BF \text{and} BE$ are equal in length.

Point $I$ is the in-centre of triangle $CEN$.

$\angle CEI=28°, \angle ENI=40°$

If $\angle CNI$ is represented by $2c$, and $\angle NEI$ is represented by $2b+c$, find the value of $b$.

Point $I$ is the in-centre of triangle $CEN$.

If $\angle CEN=60°$ and $\angle ECN=68°$, then $\angle CNI$ is,

If in a triangle $ABC,\angle A=5\angle B=8\angle C.$ Then measurement of $\angle C$Is .

The sides $AB$ and $AC$ of a triangle $ABC$are extended to $D$ and $E$ respectively. Two bisectors of the angles $\angle DBC$ and $\angle ECB$ intersect each other at $O.$ If $\angle A=30°$, then $\angle BOC=65°$ (in degrees)

In the given figure, $\mathrm{AP}$ is perpendicular to $\mathrm{BC}$, and $\mathrm{AQ}$ is the bisector of angle $\mathrm{A}$. What will be the measure of angle $\mathrm{PQA}$?