$ABCD$ is a cyclic quadrilateral in which $\angle BCD = 100^o$ and $\angle ABD = 70^o$, find $\angle ADB$.
Given:
$ABCD$ is a cyclic quadrilateral in which $\angle BCD = 100^o$ and $\angle ABD = 70^o$.
To do:
We have to find $\angle ADB$.
Solution:
$ABCD$ is a cyclic quadrilateral.
Join $BD$.
$\angle BCD = 100^o$ and $\angle ABD = 70^o$
$\angle A + \angle C = 180^o$ (Sum of the opposite angles of cyclic quadrilateral)
$\angle A+ 100^o = 180^o$
$\angle A= 180^o - 100^o$
$\angle A = 80^o$
In $\triangle ABD$,
$\angle A + \angle ABD + \angle ADB = 180^o$ (Sum of angles of a triangle)
$80^o + 70^o + \angle ADB = 180^o$
$150^o +\angle ADB = 180^o$
$\angle ADB = 180^o- 150^o$
$= 30^o$
Hence $ADB = 30^o$.
- Related Articles
- In the figure, $ABCD$ is a cyclic quadrilateral. If $\angle BCD = 100^o$ and $\angle ABD = 70^o$, find $\angle ADB$."\n
- $ABCD$ is a cyclic quadrilateral in which $\angle DBC = 80^o$ and $\angle BAC = 40^o$. Find $\angle BCD$.
- $ABCD$ is a cyclic quadrilateral in which $BC \| AD, \angle ADC =110^o$ and $\angle BAC = 50^o$. Find $\angle DAC$.
- In the figure, $ABCD$ is a cyclic quadrilateral in which $AC$ and $BD$ are its diagonals. If $\angle DBC = 55^o$ and $\angle BAC = 45^o$, find $\angle BCD$."\n
- In a cyclic quadrilateral ABCD, $\angle A = (2x+ 4)^o, \angle B = (y + 3)^o, \angle C = (2y+10)^o$ and $\angle D = (4x - 5)^o$. Find the four angles.
- In a cyclic quadrilateral $ABCD$, if $AB \| CD$ and $\angle B = 70^o$, find the remaining angles.
- ABCD is a cyclic quadrilateral such that $\angle A = (4y + 20)^o, \angle B = (3y – 5)^o, \angle C = (4x)^o$ and $\angle D = (7x + 5)^o$. Find the four angles.
- $ABCD$ is a parallelogram in which $\angle A = 70^o$. Compute $\angle B, \angle C$ and $\angle D$.
- In the figure, $ABCD$ is a parallelogram in which $\angle DAB = 75^o$ and $\angle DBC = 60^o$. Compute $\angle CDB$ and $\angle ADB$."\n
- In a cyclic quadrilateral $ABCD$, if $\angle A - \angle C = 60^o$, prove that the smaller of two is $60^o$.
- $ABCD$ is a rectangle with $\angle ABD = 40^o$. Determine $\angle DBC$.
- In a cyclic quadrilateral $ABCD$, if $m \angle A = 3(m \angle C)$. Find $m \angle A$.
- The exterior angle PRS of triangle PQR is $105^o$. If $\angle Q=70^o$, find $\angle P$. Is $\angle PRS > \angle P$.
- $ABCD$ is a cyclic quadrilateral whose diagonals intersect at a point $E$. If $\angle DBC =70â°$, $\angle BAC=30â°$. Find $\angle BCD$. Further if $AB=BC$, find $\angle ECD$.
- In the figure, lines $AB$ and $CD$ intersect at $O$. If $\angle AOC + \angle BOE = 70^o$ and $\angle BOD = 40^o$, find $\angle BOE$ and reflex $\angle COE$."\n
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies