MCQ
In a $\triangle\text{ABC},$ if $\angle\text{A}−\angle\text{B}=42^\circ$ and $\angle\text{B}−\angle\text{C}=21^\circ$ then $\angle\text{B} = ?$
- A$63^\circ$
- B$32^\circ$
- C$95^\circ$
- ✓$53^\circ$
✓
Answer
Correct option: D.
$53^\circ$
Let,
$\angle\text{A}−\angle\text{B}=42^\circ ...\ \text{(i)}$ and
$\angle\text{B}−\angle\text{C}=21^\circ ...\ \text{(ii)}$
Adding $(i)$ and $(ii)$,we get
$\angle\text{A}−\angle\text{C}=63^\circ ...\ \text{(iii)}$
$\angle\text{B}=\angle\text{A}−42^\circ$ [using $(i)]$
$\angle\text{C}=\angle\text{A}−63^\circ$ [Using $(iii)]$
$\therefore \angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ [Sum of the angles of a triangle]
$\Rightarrow \angle\text{A}+\angle\text{A}−42^\circ+\angle\text{A}−63^\circ=180^\circ$
$\Rightarrow 3\angle\text{A}−105^\circ=180^\circ$
$\Rightarrow 3\angle\text{A}=285^\circ$
$\therefore \angle\text{B}=(95−42)^\circ$
$\Rightarrow \angle\text{B}=53^\circ$
$\angle\text{A}−\angle\text{B}=42^\circ ...\ \text{(i)}$ and
$\angle\text{B}−\angle\text{C}=21^\circ ...\ \text{(ii)}$
Adding $(i)$ and $(ii)$,we get
$\angle\text{A}−\angle\text{C}=63^\circ ...\ \text{(iii)}$
$\angle\text{B}=\angle\text{A}−42^\circ$ [using $(i)]$
$\angle\text{C}=\angle\text{A}−63^\circ$ [Using $(iii)]$
$\therefore \angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ [Sum of the angles of a triangle]
$\Rightarrow \angle\text{A}+\angle\text{A}−42^\circ+\angle\text{A}−63^\circ=180^\circ$
$\Rightarrow 3\angle\text{A}−105^\circ=180^\circ$
$\Rightarrow 3\angle\text{A}=285^\circ$
$\therefore \angle\text{B}=(95−42)^\circ$
$\Rightarrow \angle\text{B}=53^\circ$
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
If $\text{x}=3+\sqrt{8}$ then $\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)=?$
→If bisector of $\angle A$ and $\angle B$ of a quadrilateral $\text{ABCD}$ intersect each other at $p , \angle B$ and $\angle C$ at $Q , \angle C$ and $\angle D$ at R and, $\angle D$ and $\angle A$ at S then $\text{PQRS}$ is a
→In a circle, the major arc is $3$ times the minor arc. The corresponding central angles and the degree measures of two arcs are:
→In figure, $ABCD$ and $AEFG$ are both parallelograms if $\angle\text{C} = 80^\circ,$ then $\angle\text{DGF}$ is: 
→In Fig. if lines / and I are parallel, then x =
The sides of a triangle are 11 m, 60 m and 61 m. The altitude to the smallest side is
The name of the horizontal line drawn to determine the position of any point in the Cartesian plane is:
A cuboid is $12\ cm$ long, $9\ cm$ broad and $8\ cm$ high. Its total surface area is:
→In the given figure, $AB \| CD$. If $\text{AOC}=30^\circ$ and $\angle\text{OAB}=100^\circ$ then $\angle\text{OCD}=?$ 
→If $(x-1)$ is a factor of polynomial $f(x)$ but not of $g(x)$, then it must be a factor of
→