MCQ
In $\triangle\text{ABC},$ if $\angle\text{A}=100^\circ,\text{AD}$ bisects $\angle\text{A}$ and $\text{AD}\perp\text{BC}.$ Then, $\angle\text{B}=$
- A$50^\circ$
- B$90^\circ$
- ✓$40^\circ$
- D$100^\circ$
✓
Answer
Correct option: C.
$40^\circ$
$\text{AD}\perp\text{BC}$ and $AD$ bisects $\angle\text{A}.$
$\Rightarrow\angle\text{BAD}=\angle\text{CAD}=50^\circ$
In Right $\triangle\text{ADB}$
$\angle\text{BAD}=50^\circ,\angle\text{ADB}=90^\circ$
Also sum of all interior angles $= 180^\circ$
$\Rightarrow\angle\text{BAD}+\angle\text{ADB}+\angle\text{B}=180^\circ$
$\Rightarrow\angle\text{B}=180^\circ-50^\circ-90^\circ$
$\Rightarrow\angle\text{B}=40^\circ$
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
An angle is $4$ time its complement. Find measure.
→In the given graph, the number of students who scored $60$ or more marks is:
→Write the correct answer in the following:
The graph of the linear equation $2x + 3y = 6$ cuts the $Y-$axis at the point,
→The graph of the linear equation $2x + 3y = 6$ cuts the $Y-$axis at the point,
How many digits are there in the repeating block of digits in the decimal expansion of $\frac{17}{7}?$
→In the following, write the correct answer. In $\triangle\text{ABC}$ and $\triangle\text{PQR},$ if $AB = AC,$ $\angle\text{C}=\angle\text{P}$ and $\angle\text{B}=\angle\text{Q}$ then the two triangles are:
→In the which quadrant does the point $(-7, -4)$ lie?
→If point $C$ lies between two points $A$ and $B$ such that $AC = BC$, then:
→In a triangle, an exterior angle at a vertex is $95^\circ $ and its one of the interior opposite angle is $55^\circ ,$ then the measure of the other interior angle is:
→If $\frac{2^{\text{m}+\text{n}}}{2^{\text{n}-\text{m}}}=16,\ \frac{3^\text{p}}{2^\text{n}}=81$ and $\text{a}=2^{\frac{1}{10}},$ then $\frac{\text{a}^{2\text{m}+\text{n}-\text{p}}}{(\text{a}^{\text{m}-2\text{n}+2\text{p}})^{-1}}=$
→What is the maximum length of a pencil that can be placed in a rectangular box of dimensions $(8\ cm × 6\ cm × 5\ cm)? ($Given $\sqrt{5}=2.24.$)
→