MCQ
In a $\triangle \text{ABC},$ if $\angle \text{A}-\angle \text{B}=33^\circ$ and $\angle \text{B}-\angle \text{C}=10^\circ,$ then $\angle \text{B} =$
- A$35^\circ$
- B$45^\circ$
- C$55^\circ$
- ✓$25^\circ$
✓
Answer
Correct option: D.
$25^\circ$
$\angle \text{A}-\angle \text{B}=33^\circ$ and $\angle \text{B}-\angle \text{C}=18^\circ$
$\Rightarrow \angle \text{A}=\angle \text{B}+33^\circ$ and $\angle \text{C}=\angle \text{B}-18^\circ$
Now, $\angle \text{A}+\angle \text{B}+\angle \text{C}=180^\circ$ [Angle sum property of triangle]
$\Rightarrow \angle \text{B}+33^\circ+\angle \text{B}+\angle \text{B}-18^\circ=180^\circ$
$\Rightarrow 3\angle \text{B}+15^\circ=180^\circ$
$\Rightarrow 3\angle \text{B}=165^\circ$
$\Rightarrow \angle \text{B}=55^\circ$
Hence, the correct answer is option $(d).$
$\Rightarrow \angle \text{A}=\angle \text{B}+33^\circ$ and $\angle \text{C}=\angle \text{B}-18^\circ$
Now, $\angle \text{A}+\angle \text{B}+\angle \text{C}=180^\circ$ [Angle sum property of triangle]
$\Rightarrow \angle \text{B}+33^\circ+\angle \text{B}+\angle \text{B}-18^\circ=180^\circ$
$\Rightarrow 3\angle \text{B}+15^\circ=180^\circ$
$\Rightarrow 3\angle \text{B}=165^\circ$
$\Rightarrow \angle \text{B}=55^\circ$
Hence, the correct answer is option $(d).$
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
Mark $(\checkmark)$ against the correct answer in the following: $\frac{-102}{119}$ in standard form is:
→Additive inverse of $\frac{2}{3}$ is
→The decimal form of 729 hundredths is-
The number of lines of symmetry for a line segment are _____.
What is the shape of each face of a cuboid?
By how much does $5$ exceed $-4$?
→In the given figure, side $B C$ of $\triangle A B C$ is produced to $D$ such that $\angle A B C=70^{\circ}$ and $\angle A C D=120^{\circ}$. Then, $\angle B A C=$ ?
→Subtract $– xy$ from $xy:$
→The reciprocal of a proper fraction is
The circumference of a circle is $44\ cm.$ Its area is:
→