Question
Line segments $AB$ and $CD$ intersect at $O$ such that $AC$ perpendicular $DB$. It $\angle \text{CAB}=35^\circ$ and$ \angle \text{CDB}=55^\circ$. Find $\angle \text{BOD}$
✓
Answer
We know that $AC$ parallel to $BD$ and $AB$ cuts $AC$ and $BD$ at $A$ and $B$, respectively.
$\angle \text{CAB}=\angle \text{DBA}$ (Alternate interior angles) $\angle \text{DBA}=35^\circ$
We also know that the sum of all three angles of a triangle is $180^\circ $
Hence, for $\triangle \text{OBD},$
we can say that: $\angle \text{DBO}+\angle \text{ODB}+\angle \text{BOD}=180^\circ$
$35^\circ+55^\circ+\angle \text{BOD}=180^\circ$
$(\angle \text{DBO}=\angle \text{DBA}$ and $\angle \text{ODB}=\angle \text{CDM})$
$\angle \text{BOD}=180^\circ-90^\circ$ $\angle \text{BOD}=90^\circ$
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
Simplify the following algebraic expressions by removing grouping symbols.
$2 a-[4 b-\{4 a-3(2 a-b)\}]$
→$2 a-[4 b-\{4 a-3(2 a-b)\}]$
For a particular show in a circus, each ticket costs $\text{Rs. }35\frac{1}{2}$ If $308$ tickets are sold for the show, how much amount has been collected?
→Subtract $(2a - 3b + 4c)$ from the sum of $(a + 3b - 4c), (4a - b + 9c)$ and $(-2b + 3c - a).$
→The circumference of a circle is $264\ cm$. Find its area.
→If angles of a triangle are in the ratio 2 : 3 : 4. Find the value of each angle.
Find the value of the unknown exterior angle $x$ in the diagram:
→Find the area enclosed by the following figure: 
The radius of one circular field is 5 m and that of the other is 13 m. Find the radius of the circular field whose area is the difference of the areas of first and second field.
In Fig. $OA$ and $OB$ are the opposite rays: If $x = 25^\circ $, what is the value of $y$?
→Find the difference of:
$\frac{18}{20}$ and $\frac{21}{25}$
→$\frac{18}{20}$ and $\frac{21}{25}$