MCQ
In Fig. if $\text {DC}\parallel\text{DC}$ and $\text{AB}=\text{AC},$ the value of $\angle\text{ABD}$ is:
- A$70^\circ$
- ✓$110^\circ$
- C$120^\circ$
- D$130^\circ$
✓
Answer
Correct option: B.
$110^\circ$
If $\text{AE}\parallel\text{DC}$ and $AC$ is transversal,
then $\angle\text{FAC}=70^\circ$ (opposite angles)
Also $\angle\text{FAC}-=\angle\text{ACB}=70^\circ$ (Alternate angles)
Since $\text{AB}=\text{AC},\triangle\text{ABC}$ is isosceles.
So $\angle\text{ABC}=\angle\text{ACB}$
$\Rightarrow\angle\text{ABC}=70^\circ$
Now $\angle\text{ABD}=180^\circ-\angle\text{ABC}=180^\circ-70^\circ=100^\circ$
Hence, correct option is (b).
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
If $a + b + c = 0$ then $\Big(\frac{\text{a}^2}{\text{bc}}+\frac{\text{b}^2}{\text{ca}}+\frac{\text{c}^2}{\text{ab}}\Big)=?$
→$(27)^{-\frac{2}{3}}$ is Equal to:
→The altitude of a circular cylinder is increased six times and the base area is decreased one-ninth of its value. The factor by which the lateral surface of the cylinder increases, is:
In a frequency distribution, ogives are graphical representation of:
Zero of the polynomial $p(x) = 2x + 5$ is:
→The number of surfaces of a cone has, is
The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
Write the correct answer in the following:
Euclid belongs to the country:
Euclid belongs to the country:
If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq. cm) is
The area of the triangle formed by the points $P(0, 1), Q(0, 5)$ and $R(3, 4)$is:
→