MCQ
In $\triangle\text{ABC},\angle\text{B}=\angle\text{C}$ and ray $AX$ bisects the exterior angle $\angle\text{DAC}.$ If $\angle\text{DAX}=70^\circ$ then $\angle\text{ACB}=$
- A$35^\circ$
- B$90^\circ$
- ✓$70^\circ$
- D$55^\circ$
✓
Answer
Correct option: C.
$70^\circ$
$AX$ is bisector of $\angle\text{DAC}.$
$\Rightarrow\angle\text{DAX}=\angle\text{XAC}=70^\circ$
$\Rightarrow\angle\text{DAC}=2\times70^\circ=140^\circ$
Now, $\angle\text{A}=180^\circ-\angle\text{DAC}=180^\circ-140^\circ=40^\circ$
In $\triangle\text{ABC},$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$\Rightarrow40^\circ+\angle\text{B}+\angle\text{C}=180^\circ$
$\Rightarrow40^\circ+\angle\text{C}+\angle\text{C}=180^\circ\dots(\angle\text{B}=\angle\text{C})$
$\Rightarrow2\angle\text{C}=140^\circ$
$\Rightarrow\angle\text{C}=70^\circ$
$\text{i.e}\angle\text{ACB}=70^\circ$
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
One of the factors of $\left(25 x^2-1\right)+(1+5 x)^2$ is:
→The number of consecutive zeros in $2^3 \times 3^4 \times 5^4 \times 7$, is:
→The statement that 'the lines are parallel if they do not intersect' is in the form of:
The number of dimensions of a solid are:
In a trapezium $ABCD$, if $AB || CD$, then $(AC^2 + BD^2) = ?$
→In the given figure, $\text{AOB}$ is a diameter of a circle and $CD \| AB$. If $\angle\text{BAD}=30^\circ$ then $\angle\text{CAD}=?$
→The value of $x^{p-q}.x^{q-r}⋅x^{r-p}$ is equal to:
→If the base radius and the height of a right circular cone are increased by $20\%,$ then the percentage increase in volume is approximately:
→If $\text{x}=\frac{\sqrt{7}}{5}$ and $\frac{5}{\text{x}}=\text{p}\sqrt{7}$ then the value of $p$ is:
→Which of the following is a rational number?