MCQ
Two lines $AB$ and $CD$ intersect at $O$. If $\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=270^\circ,$then $\angle\text{AOC}=$
- A$70^\circ$
- B$80^\circ$
- ✓$90^\circ$
- D$180^\circ$
✓
Answer
Correct option: C.
$90^\circ$
$\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=270^\circ$ [Given]
From figure,
$\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}+\angle\text{DOA}=360^\circ$
$\Rightarrow\ 270^\circ+\angle\text{DOA}=360^\circ$
$\Rightarrow\ \angle\text{DOA}=360^\circ-270^\circ=90^\circ$
Now,
$\angle\text{DOA}+\angle\text{AOC}=180^\circ$
$\Rightarrow\ \angle\text{AOC}=180^\circ-90^\circ=90^\circ$
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
The diagonals of a rhombus measure $4\ cm$ and $6\ cm$ respectively. Its area in $sq.cm$ is:
→The value of m for which $\left[\left\{\left(\frac{1}{7^2}\right)^{-2}\right\}^{-1 / 3}\right]^{1 / 4}=7^m$, is
→If each bag containing rice occupies $2.1m^3$ of space, then the number of full bags which can be emptied into a drum of radius $4.2m$ and height $3.5m$ is:
→The perpendicular distance of the point P (4, 3) from x-axis is
The graph of $y = 5$ is a line.
→In the given figure $, \text{ABCD}$ is a parallelogram in which $\angle BDC =45^{\circ}$ and $\angle BAD =75^{\circ}$. Then, $\angle CBD =$ ?
→If the perimeter of an equilateral triangle is $180\ cm$. Then its area will be:
→In a frequency distribution, the mid-value of a class is $15$ and the class intervals is $4$. The lower limit of the class is:
→$ABCD$ is a quadrilateral whose diagonal $AC$ divides it into two parts, equal in area, then $ABCD$ is:
→If $x+2$ and $x-1$ are the factors of $x^3+10 x^2+m x+n$, then the values of $m$ and $n$ are respectively
→