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 $\angle\text{B} = ?$
- A63º
- B32º
- C95º
- D53º
✓
Answer
- 53º
Solution:
Let,
$\angle\text{A}−\angle\text{B}=42°...\ \text{(i)}$ and
$\angle\text{B}−\angle\text{C}=21^\circ ...\ \text{(ii)}$
Adding (i) and (ii),we get
$\angle\text{A}−\angle\text{C}=63° ...\ \text{(iii)}$
$\angle\text{B}=\angle\text{A}−42^\circ$ [using (i)]
$\angle\text{C}=\angle\text{A}−63^\circ$ [Using (iii)]
$∴\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ [Sum of the angles of a triangle]
$⇒\angle\text{A}+\angle\text{A}−42^\circ+\angle\text{A}−63^\circ=180^\circ$
$⇒3\angle\text{A}−105^\circ=180^\circ$
$⇒3\angle\text{A}=285^\circ$
$∴\angle\text{B}=(95−42)^\circ$
$⇒\angle\text{B}=53^\circ$
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
The decimal form of $\frac{2}{11}$ is:
→In the given figure, BO and CO are bisectors of $\angle\text{B}$ and $\angle\text{C}$ respectively. If $\angle\text{A}=50^\circ$ then $\angle\text{BOC}=?$
→- 130º
- 100º
- 115º
- 120º
Which of the following is the greatest?
The area of the floor of a room is 15m2. If its height is 4m, them the volume of the air contained in the room is:
ABCD is a rhombus such that $\angle A C B=40^{\circ}$. Then, $\angle A D B=$
→The side faces of pyramid are :
In Fig. ABC is an isosceles triangle whose side AC is produced to E. Through C, CD is drawn parallel to BA. The value of x, is
How many bricks will be required to construct a wall 8m long, 6m high and 22.5cm thick if each brick measures (25cm × 11.25 × 6cm)?
- 4800
- 5600
- 6400
- 5200
If $x^{101}+101$ is divided by $x+1$, then the remainder is
→A rational number between -3 and 3 is:
- 0
- -4.3
- -3.4
- 1.101100110001...