Question

the measure of angles of triangle are in the ratio 2:3:5: find thier measures in radians

Answer 1

HEYA!
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$let \: the \: angles \: be \: 2x \: \: 3x \: \: and \: \: 5x$



❇BY ANGLE SUM PROPERTY ❇


$2x + 3x + 5x = 180 \\ \\ 10x = 180 \\ \\ = > x = 18$
Hence ,the angles in Degrees are ;

✔2×18 = 36 degrees

✔3 × 18 = 54 degrees

✔5×18 = 90 degrees .


❇RADIAN MEASURES ❇


$formula \: = \\ \\ radian \: measure = \frac{\pi}{180} \times degree \: \: \: measure \\ \\ |1| .36 \: degrees \: \\ = > \frac{\pi}{180} \times 36 = \frac{\pi}{5} radians \\ \\ \\ |2| \: \: 54 \: \: degrees \: \\ \\ = > \frac{\pi}{180} \times 54 = \frac{3\pi}{10} radians$

$|3| \: \: 90 \: degrees \: \\ = > \frac{\pi}{180} \times 90 = \frac{\pi}{2} radians$
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Answer 2

Answer:

let x be the constant angle

therefore , the ratio will

2x + 3x + 5x

Now , by sum of angle of triangle property

2x+ 3x + 5x = 180

10x = 180

x = 18

2 x 18 = 36

3 x 18 = 54

5 x 18 = 90