In figure below, $\angle ABC = 69^o, \angle ACB = 31^o$, find $\angle BDC$.
"
Given:
$\angle ABC = 69^o, \angle ACB = 31^o$
To do:
We have to find $\angle BDC$.
Solution:
We know that,
Angles in the same segment of a circle are equal.
This implies,
$\angle BAC = \angle BDC$
In $\triangle ABC$,
$\angle ABC+\angle BAC+\angle ACB = 180^o$ (The sum of the angles of a triangle is $180^o$)
$69^o+\angle BAC+31^o=180^o$
$\angle BAC = 180^o-100^o$
$\angle BAC = 80^o$
This implies,
$\angle BAC=\angle BDC = 80^o$
Hence, $\angle BDC = 80^o$.
- Related Articles
- In the figure, if $\angle ACB = 40^o, \angle DPB = 120^o$, find $\angle CBD$."\n
- In a $\triangle ABC, \angle ABC = \angle ACB$ and the bisectors of $\angle ABC$ and $\angle ACB$ intersect at $O$ such that $\angle BOC = 120^o$. Show that $\angle A = \angle B = \angle C = 60^o$.
- In the figure, if $\angle BAC = 60^o$ and $\angle BCA = 20^o$, find $\angle ADC$."\n
- In a $\triangle ABC$, if $\angle A = 55^o, \angle B = 40^o$, find $\angle C$.
- In the figure, if $ABC$ is an equilateral triangle. Find $\angle BDC$ and $\angle BEC$."\n
- In a $\triangle ABC$, $\angle A = x^o, \angle B = (3x– 2)^o, \angle C = y^o$. Also, $\angle C - \angle B = 9^o$. Find the three angles.
- 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
- In the figure, $\angle BAD = 78^o, \angle DCF = x^o$ and $\angle DEF = y^o$. Find the values of $x$ and $y$."\n
- In the figure, it is given that $O$ is the centre of the circle and $\angle AOC = 150^o$. Find $\angle ABC$."\n
- In the figure, $AB = AC$ and $\angle ACD = 105^o$, find $\angle BAC$."\n
- In the figure, $O$ is the centre of the circle. If $\angle APB = 50^o$, find $\angle AOB$ and $\angle OAB$."\n
- In the figure, $ABCD$ is a cyclic quadrilateral. If $\angle BCD = 100^o$ and $\angle ABD = 70^o$, find $\angle ADB$."\n
- In the figure, $\angle AOF$ and $\angle FOG$ form a linear pair. $\angle EOB = \angle FOC = 90^o$ and $\angle DOC = \angle FOG = \angle AOB = 30^o$.Find the measures of $\angle FOE\n
- $O$ is the centre of the circle. If $\angle ACB=40^{\circ}$, then find $\angle AOB$."\n
- In figure below, $\angle PQR = 100^o$, where $P, Q$ and $R$ are points on a circle with centre $O$. Find $\angle OPR$."\n
Kickstart Your Career
Get certified by completing the course
Get Started