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प्रश्न
Two angles of a triangle are `(5pi^"c")/9` and `(5pi^"c")/18`. Find the degree and radian measures of third angle.
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उत्तर
We know that θc = [θ x]° The measure of two angles of a triangle are [latex] `(5pi^c)/9, (5pi^c)/18`,
i.e., `((5pi)/9 xx 180/pi)^circ"," ((5pi)/18 xx 180/pi)^circ`
i.e., 100°, 50°
Let the measure of third angle of the triangle be x°.
∴ 100° + 50° + x° = 180° …[Sum of the angles of a triangle is 180°.]
∴ x° = 180° – 100° – 50°
∴ x° = 30°
= `(30 xx pi/180)^c ....[∵ theta xx pi/180]^c`
= `(pi/6)^c`
∴ The degree and radian measures of the third angle are 30° and `(π/6)^c` respectively.
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