To do:We have to find the angle which is equal to its complement.Solution:Two angles are said to be complementary if the sum of their measures is $90^o$.Let the required angle be $x^{\circ}$This implies, Its complement$=(90-x)^{\circ}$Therefore, $(90-x)^{\circ}=x^{\circ}$$(x+x)^{\circ}=90^{\circ}$$2x^{\circ}=90^{\circ}$Therefore, $x=\frac{90^{\circ}}{2}$$x=45^{\circ}$Hence, the angle which is equal to its complement is $45^{\circ}$.Read More

To do:We have to find the angle which is equal to its supplement.Solution:Two angles are said to be supplementary if the sum of their measures is $180^o$.Let the required angle be $x^{\circ}$This implies, Its supplement$=(180-x)^{\circ}$Therefore, $x^{\circ}=(180-x)^{\circ}$$(x+x)^{\circ}=180^{\circ}$$2x^{\circ}=180^{\circ}$$x^{\circ}=\frac{180^{\circ}}{2}$$x^{\circ}=90^{\circ}$Hence, the angle which is equal to its supplement is $90^{\circ}$.Read More

Given:$\angle 1$ and $\angle 2$ are supplementary angles.To do:We have to find the changes that should take place in $\angle 2$ so that both the angles still remain supplementary when $\angle 1$ is decreased.Solution:$\angle 1+\angle 2=180^{\circ}$If $\angle 1$ is decreased by some degrees, then $\angle2$ must be increased by the ... Read More

To do:We have to find the supplement of each of the given angles.Solution:Two angles are said to be supplementary if the sum of their measures is $180^o$.Supplement of an angle $x$ is $180^o-x$(i) Supplement of $105^{\circ}$$= 180^{\circ}-105^{\circ}$$=75^{\circ}$(ii) Supplement of $87^{\circ}$$= 180^{\circ}-87^{\circ}$$=93^{\circ}$(iii) Supplement of $154^{\circ}$$= 180^{\circ}-154^{\circ}$$=26^{\circ}$Read More

To do:We have to find the complement of each of the given angles.Solution:Two angles are said to be complementary if the sum of their measures is $90^{\circ}$.If two angles are complementary, each angle is said to complement of the other angle.Complement of an angle $x$ is $90^{\circ}-x$.Therefore, (i) Complement of ... Read More

To do:We have to write the given decimals as fractions in the lowest terms.Solution:Converting decimal to fraction:To convert a Decimal to a Fraction follow these stepsStep 1: Write down the decimal divided by 1.Step 2: Multiply both top and bottom by 10 for every number after the decimalpoint. (For example, if there ... Read More

Here given, Current $i=5\ A$Voltage $V=220\ Volt$Time $t=2\ hour=2\times60\times60=7200\ s$So, the power of the motor $P=Vi$$=220\ Volt\times 5\ A$$=1100\ Watt$$=1.1\ kW$                 [we know that $1\ kW=1000\ Watt$]So, energy consumed by the motor $E=Pt$$=1.1\ kW\times 2\ hour$ $=2.2\ kWh$Therefore, the electric motor consumed $2\ kWh$ ... Read More

Given:The product of the two numbers is 80.One of the numbers is 4 times the other.To do:We have to find both numbers.Solution:Let one number be $x$.This implies, The other number $=4\times x$$=4x$The product of the two numbers is 80.This implies, $x \times 4x=80$$4x^2=80$$x^2=\frac{80}{4}$$x^2=20$$x=\sqrt{20}$$x=\sqrt{4\times5}$$x=2\sqrt5$$4x=4(2\sqrt5)=8\sqrt5$Therefore, the required numbers are $2\sqrt5$ and $8\sqrt5$.    Read More

First of all we will take a beaker. Now, we will fill it partly with some water. Then, add some lycopodium powder to the beaker. Now, we will stir the contents of a beaker with a glass rod. After stirring well we will take out a few drops of this ... Read More

The formula of the resistance of a conductor is-$\boxed{R=\rho(\frac{L}{A})}$Here, $R\rightarrow$ resistance of the conductor$\rho\rightarrow$ resistivity of the conductor$L\rightarrow$length of the conductor$A\rightarrow$area of the cross-section of the conductorWe know the formula of the area of a circle, $A=\pi r^2$Or $A=\pi (\frac{d}{2})^2$            [$d$ is the diameter of ... Read More