Question

Q.10 The measures of the angles of a
triangle are in A.P. and the greatest is
5 times the smallest (least). Find the
angles in degree and radian.​

Answer 1

Answer:

Since the angles are in A.P

Let the angles be x-d, x, x+ d. (Where d= common difference)

ATQ, Greatest is 5 times the least, which means-

⇒x+ d = 5( x- d)

⇒x+ d= 5x - 5d

⇒ 4x = 6d

⇒ d= 4x/ 6

Now, we know that the sum of these angles will be 180° (Angle Sum Property)

⇒ x-d + x + x+ d= 180

⇒ 3x = 180

⇒ x= 60

So d= (4* 60) /6

= 240/6

= 40

Thus the angles will be 20°, 60°, 100°

Answer 2

Given:-

angle of triangle are in A.P

The greatest is 5 times the smallest.

To find:-

Angle in degree and radian.

Solution:-

Let the angle of triangle be a, a + d, a + 2d

• they are in A.P Sum of measure of angle of triangle is 180°.

a + a + d + a + 2d = 180°

3d + 3a = 180

3(a + d) = 180

a + d = 180/3

a + d = 60 .....(1)

• According to the Condition

• the greatest angle is 5 times the smallest

=> 5a = a + 2d

5a - a = 2d

4a - 2d = 0

2a - d = 0 × 2

2a - d = 0 ........(2)

• Adding the eq 1 and 2

a + d = 60

2a - d = 0

3a = 60

a = 60/3 = 20°

a = 20°

• substituting a = 20° in eq 2

2(20) - d = 0

40 - d = 0 40 = d

d = 40°

• Angle in degree and radian:-

a = 20° = (20° × π/180°)c = π/9 c

a + d = (20 + 40) = 60° = (60° × π/180°)c = π/3 c

a + 2d = (20 + 2 × 40) = 100° = (100° × π/180°)c = 5π/9 c