In the following figure,$\angle DBC = 70^{\circ}$ and ray $BP$ is the bisector of $\angle DBA$. Find $\angle PBC$ and reflex $\angle PBD$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Given that $\angle DBC = 70^{\circ}$ and $ABC$ is a straight line.
Therefore,$\angle DBA + \angle DBC = 180^{\circ}$ (Linear pair axiom).
$\angle DBA + 70^{\circ} = 180^{\circ} \implies \angle DBA = 110^{\circ}$.
Since ray $BP$ is the bisector of $\angle DBA$,we have $\angle ABP = \angle PBD = \frac{1}{2} \times \angle DBA = \frac{1}{2} \times 110^{\circ} = 55^{\circ}$.
Now,$\angle PBC = \angle PBD + \angle DBC = 55^{\circ} + 70^{\circ} = 125^{\circ}$.
Reflex $\angle PBD = 360^{\circ} - \angle PBD = 360^{\circ} - 55^{\circ} = 305^{\circ}$.

Explore More

Similar Questions

Find the measure of the supplementary angle of an angle of $52^{\circ}$. (in $^{\circ}$)

Prove that a triangle must have at least two acute angles.

In $\Delta ABC$,$\angle A = 2x - 10^{\circ}$,$\angle B = x + 10^{\circ}$,and $\angle C = 2x - 20^{\circ}$. Find the measure of each angle of $\Delta ABC$.

Find the measure of the complementary angle of an angle of $44^{\circ}$. (in $^{\circ}$)

In $\Delta ABC$,the sides $AB$ and $AC$ are produced to $D$ and $E$ respectively,so that exterior angles $\angle CBD$ and $\angle BCE$ are formed. If bisectors of $\angle CBD$ and $\angle BCE$ intersect at point $O$,prove that $\angle BOC = 90^{\circ} - \frac{1}{2} \angle A$.

Difficult
View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo