Q.The angles of a triangle are in the ratio $1:3:5$. The smallest in radian will be

Showing the 12 most recent of 19 on this concept.

1. CBSE 2026Set ANNUAL1 markMCQ
   Q.Radian measure of $40°20'$ is

   (a) $\dfrac{12\pi}{540}$

   (b) $\dfrac{121\pi}{540}$

   (c) $\dfrac{\pi}{540}$

   (d) None of these

   ›Reveal solutionSolution

   Convert minutes to a decimal degree, then multiply by $\pi/180$ to get radians.

   First express $40°20'$ as a single degree value. Since $1° = 60'$, $20' = \dfrac{20}{60}° = \dfrac{1}{3}°$. So

   $40°20' = \left(40 + \dfrac{1}{3}\right)° = \dfrac{121}{3}°$ …

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2. CBSE 2026Set ANNUAL1 markMCQ
   Q.Radian measure of $120°$ is —

   (a) $\frac{4\pi}{3}$

   (b) $\frac{\pi}{3}$

   (c) $\frac{2\pi}{3}$

   (d) $\frac{\pi}{6}$

   ›Reveal solutionSolution

   $120° = \frac{2\pi}{3}$ radians, option (c).

   To convert an angle from degrees to radians, multiply by $\frac{\pi}{180}$:

   …

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3. CBSE 2025Set ANNUAL1 markMCQ
   Q.$\dfrac{\pi}{2}$ radian $=$

   (a) $180°$

   (b) $90°$

   (c) $120°$

   (d) $360°$

   ›Reveal solutionSolution

   $\dfrac{\pi}{2}$ radian $= 90°$.

   The conversion between radians and degrees uses $\pi$ radians $= 180°$.

   …

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4. CBSE 2025Set ANNUAL1 markMCQ
   Q.Degree measure of $\left(\dfrac{3}{4}\right)^c$ is

   (a) $42°50''$

   (b) $42°57'16''$

   (c) $49°61'$

   (d) $41°57'18''$

   ›Reveal solutionSolution

   Using the standard approximation $1$ radian $\approx 57°16'22''$ (from $\pi\approx\frac{22}{7}$), three-quarters of a radian works out to $42°57'16''$.

   $\text{Degree measure} = \text{Radian measure} \times \frac{180°}{\pi}$

   Using $\pi \approx \dfrac{22}{7}$: $\dfrac{180}{\pi} \approx \dfrac{180\times7}{22} = \dfrac{1260}{22} = 57.2727...°$, i.e. $1$ radian $\approx 57°16'22''$.

   $\left(\frac34\right)^c = \frac34 \times 57.2727...° = 42.9545...°$

   Converting the decimal part to minutes/seconds:

   $0.9545° \times 60 = 57.27' \implies 42°57.27'$ …

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5. CBSE 2024Set ANNUAL1 markMCQ
   Q.The angles of a triangle are in the ratio $1:3:5$. The smallest in radian will be

   (a) $\dfrac{\pi}{9}$

   (b) $\dfrac{\pi}{3}$

   (c) $\dfrac{5\pi}{9}$

   (d) None of these

   ›Reveal solutionSolution

   Use the angle-sum property of a triangle to find each angle from the given ratio, then convert the smallest to radians.

   Let the angles be $x, 3x, 5x$ (in the ratio $1:3:5$). The angles of a triangle sum to $180^\circ$:

   $x + 3x + 5x = 180^\circ \implies 9x = 180^\circ \implies x = 20^\circ$

   So the angles are $20^\circ, 60^\circ, 100^\circ$. The smallest is $20^\circ$.

   …

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6. CBSE 2024Set ANNUAL1 mark
   Q.Convert $\dfrac{5\pi}{3}$ in radian measure.

   ›Reveal solutionSolution

   The angle $\dfrac{5\pi}{3}$ (given in radian form) equals $300^\circ$ in degree measure.

   …

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7. CBSE 2024Set ANNUAL1 markMCQ
   Q.The degree measure corresponding to $\dfrac{5\pi}{3}$ radian is:

   (a) $210^\circ$

   (b) $510^\circ$

   (c) $300^\circ$

   (d) None of these.

   ›Reveal solutionSolution

   $\dfrac{5\pi}{3}$ radians equals $300^\circ$.

   We use the relation $180^\circ = \pi$ radians, so $1$ radian $=\dfrac{180^\circ}{\pi}$. …

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8. CBSE 2024Set ANNUAL1 markMCQ
   Q.The value of $\pi$ radian is:

   (a) 60°

   (b) 180°

   (c) 90°

   (d) 45°

   ›Reveal solutionSolution

   By definition of radian measure, $\pi$ radian equals $180°$.

   Step 1. A full circle is $360°$, which corresponds to $2\pi$ radians.

   …

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9. CBSE 2023Set ANNUAL1 markMCQ
   Q.1 radian $=$

   (a) $\dfrac{\pi}{180°}$

   (b) $\dfrac{180°}{\pi}$

   (c) $180°$

   (d) $360°$

   ›Reveal solutionSolution

   Since $\pi \text{ rad} = 180°$, one radian equals $180°/\pi \approx 57.3°$.

   The relation between radian and degree measure comes from the fact that a full circle subtends an angle of $2\pi$ radians, which is also $360°$. So:

   $\pi \text{ radians} = 180°$

   …

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10. CBSE 2023Set ANNUAL1 markMCQ
    Q.The radian measure corresponding to $240°$ will be:

    (a) $\dfrac{26\pi}{9}$

    (b) $\dfrac{4\pi}{3}$

    (c) $\dfrac{5\pi}{36}$

    (d) $\dfrac{7\pi}{6}$

    ›Reveal solutionSolution

    $240° = \dfrac{4\pi}{3}$ radians.

    To convert an angle from degrees to radians, multiply by $\dfrac{\pi}{180}$:

    $240° \times \frac{\pi}{180} = \frac{240\pi}{180} = \frac{4\pi}{3}$

    …

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11. CBSE 2023Set ANNUAL1 markMCQ
    Q.Degree measure of 7π/6 is:

    (a) 30°

    (b) 11°/3

    (c) 210°

    (d) None of these

    ›Reveal solutionSolution

    Multiply the radian measure by $\dfrac{180^\circ}{\pi}$ to convert to degrees.

    Since $\pi$ radians $= 180^\circ$: …

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12. CBSE 2023Set ANNUAL1 mark
    Q.Find the degree measure corresponding to the radian measure : $\dfrac{11}{16}$. [use $\pi = \dfrac{22}{7}$].

    ›Reveal solutionSolution

    $\dfrac{11}{16}$ radians $\approx39^\circ22'30''$.

    Using $\text{degree} = \text{radian}\times\dfrac{180}{\pi}$ and $\pi=\dfrac{22}{7}$, so $\dfrac{180}{\pi}=\dfrac{180\times7}{22}=\dfrac{1260}{22}=\dfrac{630}{11}$:

    $\dfrac{11}{16}\times\dfrac{630}{11} = \dfrac{630}{16} = 39.375^\circ.$

    …

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