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Measuremenet Of Angle — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSMeasuremenet Of Angle3 Marks
Question
One angle of a triangle $\frac{2}{3}\text{x}$ grades and another is $\frac{3}{2}\text{x}$ degrees while the third is $\frac{\pi\text{x}}{75}$ radians. Express all the angles in degrees.
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Answer

Let $\theta_{1}$ $\theta_{2}$and $\theta_{3}$ be angles of a right angles triangle. $\theta_{1}=\frac{2}{3}\times\text{gradiants}$ $\theta_{2}=\frac{3}{2}\times\text{degrees}$ $\theta_{2}=\frac{\pi\text{x}}{75}\times\text{radians}$ Now, We have to express all the angles in degrees, $\theta_{1}=\Big(\frac{3}{2}\text{x}\times\frac{90}{100}\Big)^{\circ}$ $=\frac{3}{5}\text{x}$ $\theta_{2}=\frac{\pi\text{x}}{75}\times\frac{180}{\pi}$ $=\frac{12\text{x}}{5}$ By angles property, $\theta_{1}+\theta_{2}+\theta_{3}=180^{\circ}$ $\frac{3}{5}\text{x}^{\circ}+\frac{3}{2}\text{x}^{\circ}+\frac{12\text{x}}{5}=180^{\circ}$ $\Rightarrow\frac{9}{2}\text{x}^{\circ}=180^{\circ}$ $\Rightarrow \text{x}=40^{\circ}$ $\therefore\ \theta_{1}=24^{\circ},\theta_{2}=60^{\circ},\theta_{3}=96^{\circ}$

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