MCQ
The difference between two complementary angles is $400$. The angles are:
- A$70^{\circ}, 110^{\circ}$
- B$65^{\circ}, 35^{\circ}$
- ✓$65^{\circ}, 25^{\circ}$
- D$70^{\circ}, 30^{\circ}$
✓
Answer
Correct option: C.
$65^{\circ}, 25^{\circ}$
We know that the sum of two complementary angles is $90^{\circ}$Let the two angles be $x$ and $y$
$x+y=90^{\circ}(1)$
We also know that the difference of the angles is $40^{\circ}$
Therefore, $x-y=40^{\circ}(2)$
Combining $(1)$ and $(2)$
We have
$x+y=90^{\circ}$
$x-y=40^{\circ}$
Solving as simultaneous equations we get
$2 x=130^{\circ}$
Hence $x=65^{\circ}$
Substituting this value of $x$ in either one of the equations $(1)$ or $(2)$
We get $y=25^{\circ}$.
$x+y=90^{\circ}(1)$
We also know that the difference of the angles is $40^{\circ}$
Therefore, $x-y=40^{\circ}(2)$
Combining $(1)$ and $(2)$
We have
$x+y=90^{\circ}$
$x-y=40^{\circ}$
Solving as simultaneous equations we get
$2 x=130^{\circ}$
Hence $x=65^{\circ}$
Substituting this value of $x$ in either one of the equations $(1)$ or $(2)$
We get $y=25^{\circ}$.
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 $\sqrt{2}=1.41$ then $\frac{1}{\sqrt{2}}=?$
→$75 × 75 + 2 × 75 × 25 + 25 × 25$ is equal to:
→The sum of $0.\overline{3}$ and $0.\overline{4}$ is:
→The angles of a triangle are in the ratio $2 : 3 : 4$. The largest angle of the triangle is:
→The graph of a linear equation $\text{y}=\frac{9}{5}\text{x}+32$ cuts the $y-$axis at the point:
→In a circle with centre O, AB and CD are two diameters perpendicular each other. The length of chord AC, is
In the adjoining figure, $AB = AC$. If $\angle\text{ACD} = 115^\circ,$ then the measure of $\angle\text{A}$ is:
→→
$9^3+(-3)^3-6^3=?$
→In the given figure, $BOC$ is a diameter of a circle and $AB = AC.$ Then, $\angle\text{ABC}=?$ 
→