In the figure, lines $AB, CD$ and $EF$ intersect at $O$. Find the measures of $\angle AOC, \angle COF, \angle DOE$ and $\angle BOF$.
"
Given:
Lines $AB, CD$ and $EF$ intersect at $O$.
To do:
We have to find the measures of $\angle AOC, \angle COF, \angle DOE$ and $\angle BOF$.
Solution:
We know that,
Vertically opposite angles are equal.
Sum of the angles on a straight line is $180^o$.
Therefore,
$\angle AOC=\angle BOD=35^o$ (Vertically opposite angles)
$\angle BOF=\angle AOE=40^o$ (Vertically opposite angles)
$AOB$ is a straight line.
This implies,
$\angle AOE+\angle EOD+\angle BOD = 180^o$
$40^o + \angle EOD + 35^o = 180^o$
$\angle EOD= 180^o-75^o$
$\angle EOD=105^o$
$\angle COF=\angle EOD=105^o$ (Vertically opposite angles)
Hence, $\angle AOC=35^o, \angle COF=105^o, \angle DOE=105^o$ and $\angle BOF=40^o$.
- Related Articles
- 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
- Two lines $AB$ and $CD$ intersect at $O$. If $\angle AOC + \angle COB + \angle BOD = 270^o$, find the measure of $\angle AOC, \angle COB, \angle BOD$ and $\angle DOA$.
- $AB, CD$ and $EF$ are three concurrent lines passing through the point $O$ such that $OF$ bisects $\angle BOD$. If $\angle BOF = 35^o$, find $\angle BOC$ and $\angle AOD$.
- In Fig. 6.13, lines \( \mathrm{AB} \) and \( \mathrm{CD} \) intersect at \( \mathrm{O} \). If \( \angle \mathrm{AOC}+\angle \mathrm{BOE}=70^{\circ} \) and \( \angle \mathrm{BOD}=40^{\circ} \), find \( \angle \mathrm{BOE} \) and reflex \( \angle \mathrm{COE} \)."\n
- In the figure, $AB$ and $CD$ are diameiers of a circle with centre $O$. If $\angle OBD = 50^o$, find $\angle AOC$."\n
- If AB||CD and CD||EF Find $\angle$ACE"\n
- In the figure, if $AB \parallel CD$ and $CD \parallel EF$, find $\angle ACE$."\n
- In Fig $\displaystyle AB\ \parallel \ CD$ , and $EF \perp CD$ , $\angle GED = 120°$. Find $\angle GEC , \angle EGF , \angle GEF$"\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
- In the figure, $AB = AC$ and $\angle ACD = 105^o$, find $\angle BAC$."\n
- In the figure, $AB \parallel CD \parallel EF$ and $GH \parallel KL$. Find $\angle HKL$."\n
- In the following figure, if AOB is a straight line then find the measures of $\angle AOC$ and $\angle BOC$."\n
- In the figure, if $\angle BAC = 60^o$ and $\angle BCA = 20^o$, find $\angle ADC$."\n
- In the figure, $AB \parallel CD$ and $P$ is any point shown in the figure. Prove that:$\angle ABP + \angle BPD + \angle CDP = 360^o$"\n
- In the figure, rays $OA, OB, OC, OD$ and $OE$ have the common end point $O$. Show that $\angle AOB + \angle BOC + \angle COD + \angle DOE + \angle EOA = 360^o$."\n
Kickstart Your Career
Get certified by completing the course
Get Started