Question
In figure, lines $AB$ and $CD$ intersect at $O$. If $\angle\text{AOC}+\angle\text{BOE}=70^\circ$ and $\angle\text{BOD}=40^\circ,$ find $\angle\text{BOE}$ and reflex $\angle\text{COE}.$
✓
Answer
In the figure, $\angle\text{AOC},\angle\text{BOE}$ and $\angle\text{COE} $ from a linear pair.
Thus,
$\angle\text{AOC}+\angle\text{BOE}+\angle\text{COE}=180^\circ$
It is given that $\angle\text{AOC}+\angle\text{BOE}=70^\circ,$
on substituting this value, we get:
$70^\circ+\angle\text{COE}=180^\circ$
$\angle\text{COE}=180^\circ-70^\circ$
$\angle\text{COE}=110^\circ$
Thus, reflex $\angle\text{COE}=360^\circ-110^\circ$
Therefore, reflex $\angle\text{COE}=250^\circ.$
Thus,
$\angle\text{AOC}+\angle\text{BOE}+\angle\text{COE}=180^\circ$
It is given that $\angle\text{AOC}+\angle\text{BOE}=70^\circ,$
on substituting this value, we get:
$70^\circ+\angle\text{COE}=180^\circ$
$\angle\text{COE}=180^\circ-70^\circ$
$\angle\text{COE}=110^\circ$
Thus, reflex $\angle\text{COE}=360^\circ-110^\circ$
Therefore, reflex $\angle\text{COE}=250^\circ.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
How many spheres $12\ cm$ in diameter can be made from a metallic cylinder of diameter $8\ cm$ and height $90\ cm?$
→In the given figure, $O$ is the canter of the circle and $\angle\text{AOB}=70^\circ.$ Calculate the values of
$i. \angle\text{OCA}$
$ii. \angle\text{OAC}$
→$i. \angle\text{OCA}$
$ii. \angle\text{OAC}$
Two sides $AB$ and $BC$ and median $AM$ of the $\triangle ABC$ are respectively equal to side $PQ$ and $QR$ and median $PN $of $\text{PQR} ($See figure$)$. Show that:
$i. \triangle ABM \cong \triangle PQN$
$ii. \triangle ABC \cong \triangle PQR$
→$i. \triangle ABM \cong \triangle PQN$
$ii. \triangle ABC \cong \triangle PQR$
A rectangular plot is given for constructing a house, having a measurement of $40\ m$ long and $15\ m$ in the front. According to the laws, a minimum of $3\ m$, wide space should be left in the front and back each and $2\ m$ wide space on each of other sides. Find the largest area where house can be constructed.
→Evaluate the following:
$(9.9)^3$
→$(9.9)^3$
Find solutions of the form $x = a, y = 0$ and $x = 0, y = b$ for the following pairs of equations. Do they have any common such solution$?\ 3x + 2y = 6$ and $5x + 2y = 10$
→Simplify: $\big(3+\sqrt{3}\big)\big(2+\sqrt{2}\big)^2$
→In the given figure, $AB\ ||\ CD$ and $EF$ is a transversal, cutting them at $G$ and $H$ respectively. If $\angle\text{EGB}=35^\circ$ and $\text{QP}\perp\text{EF},$ find the measure of $\angle\text{PQH}.$
→ It being given that $\sqrt{3}=1.732,\sqrt{5}=2.236,\sqrt{6}=2.449$ and $\sqrt{10}=3.162,$ find to three places of decimal, the value of the following:
$\frac{1+2\sqrt{3}}{2-\sqrt{3}}$
→$\frac{1+2\sqrt{3}}{2-\sqrt{3}}$
$AD$ is a median of the $\triangle\text{ABC}.$ Is it true that $AB + BC + CA > 2AD?$ Give reason for your answer.
→