8 the sum of two angles is 5pi ^ c and their difference is 60°. find their measures in degree.

Question 16 Properties of Triangle Exercise 15.2

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Answer:

Given that one of the angles of the given triangle is 60.

Also given that the other two angles of the triangle are in the ratio 1: 2.

Let one of the other two angles be x.

Therefore, the second one will be 2x.

We know that the sum of all the three angles of a triangle is equal to 180.

60 + x + 2x = 180

3x = 180 – 60

3x = 120

x = 120/3 x = 40

2x = 2 × 40

2x = 80

Hence, we can conclude that the required angles are 40 and 80.

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We know that, 1c = `(180/pi)^circ`

∴ 5πc = `(5pi xx 180/pi)^"c"` = 900°

Let the degree measures of the angles be x and y.

Then x + y = 900°  ...(1)

and x – y = 60°  ...(2)

2x = 960°

x = 480°

Adding (1) and (2), we get,

2x = 960°  ∴ x = 480°

∴ Substituting the value of x in (1), we get480° + y = 900°

∴ y = 900° − 480°

∴ y = 420°

Hence, the degree measures of the two angles are 480° and 420°.