MCQ
The diagonals of a parallelogram $\text{ABCD}$ intersect at $O$. if $\angle\text{BOC}=90^\circ$ and $\angle\text{BDC}=50^\circ,$ then $\angle\text{AOB}=$
- ✓$40^\circ$
- B$50^\circ$
- C$10^\circ$
- D$90^\circ$
✓
Answer
Correct option: A.
$40^\circ$
In a parallelogram $\text{ABCD},$
$\angle\text{OAB}=\angle\text{OCB}$
In $\triangle\text{OCB}$
$\angle\text{OCD}+\angle\text{COD}+\angle\text{ODC}=180^\circ$
$\angle\text{COD}=90^\circ$
$\angle\text{ODC}=50^\circ \ ($given$)$
$\angle\text{OCD}=180^\circ-90^\circ-50^\circ=40^\circ$
$\Rightarrow\angle\text{OAB}=\angle\text{OCD}=40^\circ$
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
$P$ is any point on the side $BC$ of a $\triangle\text{ABC}. P$ is joined to $A$. If $D$ and $E$ are the midpoints of the sides $AB$ and $AC$ respectively and $M$ and $N$ are the midpoints of $BP$ and $CP$ respectively then quadrilateral $\text{DENM}$ is:
→If $n$ is a natural number, then $\sqrt{\text{n}}$ is:
→The median of a triangle divides it into two:
Points $\{(1, -1), (2, -2), (-3, -4), (4, -5)\}$
→The abscissa of a point is positive in the:
If $x + 2$ is a factor of $x^2 + mx + 14,$ then $m =$
→Find d(A, B), if co-ordinates of A and B are – 2 and 5 respectively.
A point whose abscissa and ordinate are $2$ and $-5$ respectively, lies in :
→What is the degree of the polynomial ?
If $A$ and $B$ are two points on a circle such that $\text{m}\big(\widehat{\text{AB}}\big)=260^\circ. A$ possible value for the angle subtended by arc $BA$ at a point on the circle is:
→