MCQ
Two complementary angles differ by $20^\circ .$ The smaller angle is:
- A$55^\circ $
- B$25^\circ$
- C$65^\circ$
- ✓$35^\circ$
✓
Answer
Correct option: D.
$35^\circ$
Let the smaller angle be $x.$
Then,The larger angle $= (x + 20^\circ )$
As, the sum of the two complementary angles is always $90^\circ .$
$\Rightarrow x + (x + 20^\circ ) = 90^\circ $
$\Rightarrow 2x + 20^\circ = 90^\circ $
$\Rightarrow 2x = 90^\circ - 20^\circ $
$\Rightarrow 2x = 70^\circ $
$\Rightarrow\text{x}=\frac{70^\circ}{2} ($By transposing $2$ to $R.H.S.)$
$\therefore\text{x}=35^\circ$
So, the smaller angle is $35^\circ .$
Hence, the correct alternative is option $(d).$
Then,The larger angle $= (x + 20^\circ )$
As, the sum of the two complementary angles is always $90^\circ .$
$\Rightarrow x + (x + 20^\circ ) = 90^\circ $
$\Rightarrow 2x + 20^\circ = 90^\circ $
$\Rightarrow 2x = 90^\circ - 20^\circ $
$\Rightarrow 2x = 70^\circ $
$\Rightarrow\text{x}=\frac{70^\circ}{2} ($By transposing $2$ to $R.H.S.)$
$\therefore\text{x}=35^\circ$
So, the smaller angle is $35^\circ .$
Hence, the correct alternative 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
The solution of the equation $y - 4 = -1$ is:
→The average of first $4$ prime numbers is$?$
→The name of the solid shape is:
The mean of p, q and r is same as the mean of q, 2r and s. Then which of the following is correct?
Mark $(✓)$ against the correct answer. The area of a square is $50cm^2$. The length of its diagonal is:
→A number with decimal point followed by $1$ or more digits is called:
→$\frac{-3}{8}+0=?$
→The number of triangular faces of a triangular prism is _______.
(-1) + (−1) + (−1) + (-1) +__________ 500 times =
The angle which is twice its supplement is: